(DEPTH-ARRAYP-AUX
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 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
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 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP-AUX-OF-MINUS1)
(DEPTH-ARRAYP-AUX-OF-0
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 (2 2 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
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 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
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(DEPTH-ARRAYP-AUX-MONOTONE
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 (23 23 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
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 (18 18 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (15 15 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (14 14 (:REWRITE DEFAULT-+-2))
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(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX
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 (28 14 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
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 (14 14 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 10 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE USE-ALL-NATP-2))
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 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
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(DEPTH-ARRAYP-AUX-OF-ASET1-TOO-HIGH
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 (60 26 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
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 (33 33 (:REWRITE DEFAULT-<-1))
 (33 33 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (24 24 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (22 22 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
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 (19 19 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (19 19 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 10 (:LINEAR ARRAY2P-LINEAR))
 (8 8 (:REWRITE DEFAULT-+-2))
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(DEPTH-ARRAYP-AUX-OF-ASET1
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 (46 46 (:REWRITE USE-ALL-<-2))
 (46 46 (:REWRITE USE-ALL-<))
 (46 46 (:REWRITE DEFAULT-<-1))
 (46 46 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (40 40 (:REWRITE USE-ALL-<=-2))
 (40 40 (:REWRITE USE-ALL-<=))
 (34 22 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (26 26 (:REWRITE DEFAULT-+-2))
 (26 26 (:REWRITE DEFAULT-+-1))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (20 20 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (20 2 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (16 6 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (12 12 (:REWRITE USE-ALL-NATP-2))
 (12 12 (:REWRITE USE-ALL-NATP))
 (12 12 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
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 (8 8 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
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 (2 2 (:DEFINITION FIX))
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(DEPTH-ARRAYP-AUX-OF-ASET1-AT-END
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 (17 17 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (13 11 (:REWRITE DEFAULT-<-2))
 (12 7 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (12 2 (:REWRITE DEPTH-ARRAYP-AUX-OF-ASET1-TOO-HIGH))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
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 (11 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE DEFAULT-<-1))
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 (10 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
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 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 2 (:REWRITE +-COMBINE-CONSTANTS))
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 (2 2 (:LINEAR ARRAY2P-LINEAR))
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(DEPTH-ARRAYP-AUX-OF-COMPRESS1
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 (36 27 (:REWRITE DEFAULT-<-1))
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 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
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 (8 8 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
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(DEPTH-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER
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 (36 18 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
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 (18 18 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
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(DEPTH-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER-IRREL
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 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
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 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
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(ENSURE-DEFAULT-SATISFIES-PRED)
(DEPTH-ARRAYP-AUX-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT
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 (14 7 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
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 (13 13 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (11 5 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP)
(ARRAY1P-WHEN-DEPTH-ARRAYP)
(DEPTH-ARRAYP-FORWARD-TO-ARRAY1P)
(DEPTH-ARRAYP-FORWARD-TO-LEN-BOUNDDEPTH-ARRAYP)
(DEPTH-ARRAYP-FORWARD-TO-LEN-BOUND-2DEPTH-ARRAYP)
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP
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 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-SPECIAL
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 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(DEPTH-ARRAYP-MONOTONE
 (8 2 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (7 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(DEPTH-ARRAYP-OF-ASET1
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 (14 11 (:REWRITE DEFAULT-<-1))
 (13 11 (:REWRITE DEFAULT-<-2))
 (12 3 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (6 2 (:REWRITE +-COMBINE-CONSTANTS))
 (5 5 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 3 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(DEPTH-ARRAYP-OF-ASET1-AT-END
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 (95 3 (:DEFINITION DEPTH-ARRAYP-AUX))
 (25 25 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (21 9 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (15 15 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE DEFAULT-+-1))
 (14 11 (:REWRITE DEFAULT-<-1))
 (13 11 (:REWRITE DEFAULT-<-2))
 (12 3 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (6 5 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (4 4 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
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(DEPTH-ARRAYP-OF-ASET1-AT-END-GEN
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 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE USE-ALL-<-2))
 (12 12 (:REWRITE USE-ALL-<))
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 (12 12 (:REWRITE DEFAULT-<-1))
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 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
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 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
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(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT
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 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
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 (5 5 (:REWRITE DEFAULT-<-1))
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 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
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(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY
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 (4 4 (:REWRITE USE-ALL-<=))
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 (4 4 (:REWRITE USE-ALL-<))
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 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
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(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-AND-0
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 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE USE-ALL-<-2))
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 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (1 1 (:REWRITE DEPTH-ARRAYP-AUX-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT))
 (1 1 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX-ALT
 (329 329 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 18 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (12 12 (:REWRITE USE-ALL-<=-2))
 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE USE-ALL-<-2))
 (12 12 (:REWRITE USE-ALL-<))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (8 8 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-ALT
 (54 54 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (3404 136 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2794 27 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (2156 110 (:DEFINITION NAT-LISTP))
 (1624 65 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (1409 63 (:REWRITE USE-ALL-<-FOR-CAR))
 (1350 65 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (1344 1344 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (1191 92 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (602 602 (:TYPE-PRESCRIPTION NAT-LISTP))
 (378 18 (:REWRITE ALL-<-OF-CDR))
 (367 367 (:TYPE-PRESCRIPTION ALL-<))
 (322 198 (:REWRITE DEFAULT-<-2))
 (298 298 (:REWRITE DEFAULT-CAR))
 (286 38 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (268 48 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (259 55 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (247 247 (:TYPE-PRESCRIPTION ALL-NATP))
 (237 3 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (231 18 (:REWRITE ALL-NATP-OF-CDR))
 (204 204 (:REWRITE USE-ALL-<-2))
 (204 204 (:REWRITE USE-ALL-<))
 (194 24 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (184 92 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (182 182 (:REWRITE USE-ALL-<=-2))
 (182 182 (:REWRITE USE-ALL-<=))
 (177 177 (:REWRITE DEFAULT-CDR))
 (171 136 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (157 55 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (136 136 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (136 136 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (136 136 (:REWRITE ALL-<-TRANSITIVE))
 (136 51 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (126 63 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (123 123 (:REWRITE USE-ALL-CONSP-2))
 (123 123 (:REWRITE USE-ALL-CONSP))
 (120 24 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (119 92 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (112 28 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (110 55 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (110 5 (:REWRITE ARRAY1P-OF-ASET1-SIMPLE))
 (109 24 (:REWRITE <-OF-CAR-AND-ALEN1))
 (102 102 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (102 102 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (102 102 (:TYPE-PRESCRIPTION ALL-CONSP))
 (102 17 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (96 96 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (92 92 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (92 63 (:REWRITE DEFAULT-+-2))
 (90 90 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (89 89 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (89 89 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (88 44 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (88 44 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (84 84 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (74 6 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (66 9 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (66 7 (:REWRITE DEPTH-ARRAYP-AUX-OF-ASET1-TOO-HIGH))
 (63 63 (:REWRITE DEFAULT-+-1))
 (55 55 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (55 55 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (55 55 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (55 55 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (54 27 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (54 27 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (51 51 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (51 51 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (51 51 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (51 51 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (48 48 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (46 46 (:LINEAR ARRAY2P-LINEAR))
 (45 45 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (44 44 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (43 43 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (43 43 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (41 41 (:REWRITE USE-ALL-RATIONALP-2))
 (41 41 (:REWRITE USE-ALL-RATIONALP))
 (41 41 (:REWRITE USE-ALL-NATP-2))
 (41 41 (:REWRITE USE-ALL-NATP))
 (36 6 (:REWRITE USE-ALL-<=-FOR-CAR))
 (27 27 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (27 27 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (26 18 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (24 24 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (16 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX-ALT))
 (15 15 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (15 3 (:REWRITE +-COMBINE-CONSTANTS))
 (12 12 (:TYPE-PRESCRIPTION ALL-<=))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<=-MONOTONE))
 (6 6 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (6 6 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (6 3 (:REWRITE UNICITY-OF-0))
 (5 5 (:REWRITE DIMENSIONS-WHEN-NOT-CONSP-OF-HEADER-CHEAP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-ALT))
 (1 1 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 )
(DEPTH-ARRAYP-OF-SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (3727 100 (:DEFINITION NAT-LISTP))
 (2241 62 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2059 91 (:REWRITE USE-ALL-<-FOR-CAR))
 (1805 108 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1112 5 (:REWRITE AREF1-OF-ASET1-BOTH))
 (759 736 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (555 555 (:TYPE-PRESCRIPTION NAT-LISTP))
 (553 66 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (465 34 (:REWRITE ALL-NATP-OF-CDR))
 (438 99 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (422 86 (:DEFINITION MEMBER-EQUAL))
 (378 24 (:REWRITE ALL-<-OF-CDR))
 (367 170 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (355 170 (:REWRITE DEFAULT-<-2))
 (273 273 (:REWRITE DEFAULT-CAR))
 (270 270 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (234 234 (:REWRITE DEFAULT-CDR))
 (216 170 (:REWRITE DEFAULT-<-1))
 (216 108 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (202 8 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (191 36 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (182 91 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (170 170 (:REWRITE USE-ALL-<-2))
 (170 170 (:REWRITE USE-ALL-<))
 (160 80 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (160 80 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (159 159 (:REWRITE USE-ALL-<=-2))
 (159 159 (:REWRITE USE-ALL-<=))
 (131 115 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (122 106 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (121 11 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (119 119 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (119 119 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (115 115 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (115 115 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (115 115 (:REWRITE ALL-<-TRANSITIVE))
 (115 18 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (105 105 (:REWRITE USE-ALL-CONSP-2))
 (105 105 (:REWRITE USE-ALL-CONSP))
 (88 33 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (80 80 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (80 80 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (80 80 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (69 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (66 66 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (66 66 (:REWRITE USE-ALL-NATP-2))
 (66 66 (:REWRITE USE-ALL-NATP))
 (66 11 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (66 11 (:REWRITE <-OF-CAR-AND-ALEN1))
 (55 11 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (46 46 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (46 46 (:TYPE-PRESCRIPTION ALL-CONSP))
 (45 35 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (38 38 (:LINEAR ARRAY2P-LINEAR))
 (36 18 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (36 6 (:REWRITE USE-ALL-<=-FOR-CAR))
 (33 33 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (33 33 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (32 16 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (32 16 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (30 30 (:REWRITE USE-ALL-RATIONALP-2))
 (30 30 (:REWRITE USE-ALL-RATIONALP))
 (25 5 (:REWRITE ALL-CONSP-OF-CDR))
 (23 23 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (23 23 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (22 22 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (18 18 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (18 18 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (18 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (18 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (16 16 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (16 12 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (15 5 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (13 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 (12 12 (:TYPE-PRESCRIPTION ALL-<=))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (11 11 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<=-MONOTONE))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:REWRITE AREF1-OF-ASET1-DIFF))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(ALEN1-OF-SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (3751 112 (:DEFINITION NAT-LISTP))
 (2265 68 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2059 91 (:REWRITE USE-ALL-<-FOR-CAR))
 (1829 114 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1120 13 (:REWRITE AREF1-OF-ASET1-BOTH))
 (1033 978 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (573 573 (:TYPE-PRESCRIPTION NAT-LISTP))
 (553 66 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (465 34 (:REWRITE ALL-NATP-OF-CDR))
 (453 168 (:REWRITE DEFAULT-<-2))
 (438 99 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (378 24 (:REWRITE ALL-<-OF-CDR))
 (276 276 (:REWRITE DEFAULT-CAR))
 (266 65 (:DEFINITION MEMBER-EQUAL))
 (259 48 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (248 248 (:REWRITE DEFAULT-CDR))
 (228 114 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (214 168 (:REWRITE DEFAULT-<-1))
 (202 8 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (195 26 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (193 193 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (192 168 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (182 91 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (168 168 (:REWRITE USE-ALL-<-2))
 (168 168 (:REWRITE USE-ALL-<))
 (160 80 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (160 80 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (159 33 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (157 157 (:REWRITE USE-ALL-<=-2))
 (157 157 (:REWRITE USE-ALL-<=))
 (143 127 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (128 112 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (127 127 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (127 127 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (127 127 (:REWRITE ALL-<-TRANSITIVE))
 (121 11 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (118 118 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (118 118 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (117 26 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (115 115 (:REWRITE USE-ALL-CONSP-2))
 (115 115 (:REWRITE USE-ALL-CONSP))
 (88 33 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (80 80 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (80 80 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (80 80 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (78 78 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (78 78 (:TYPE-PRESCRIPTION ALL-CONSP))
 (77 51 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (66 66 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (66 66 (:REWRITE USE-ALL-NATP-2))
 (66 66 (:REWRITE USE-ALL-NATP))
 (66 11 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (66 11 (:REWRITE <-OF-CAR-AND-ALEN1))
 (65 13 (:REWRITE ALL-CONSP-OF-CDR))
 (55 11 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (52 26 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (44 22 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (44 22 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (42 42 (:REWRITE USE-ALL-RATIONALP-2))
 (42 42 (:REWRITE USE-ALL-RATIONALP))
 (40 40 (:LINEAR ARRAY2P-LINEAR))
 (39 39 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (39 39 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (39 13 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (36 6 (:REWRITE USE-ALL-<=-FOR-CAR))
 (33 33 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (33 33 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (26 26 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (26 26 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (26 26 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (26 26 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (22 22 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (22 22 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (22 22 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (22 18 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (13 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE AREF1-OF-ASET1-DIFF))
 (12 12 (:TYPE-PRESCRIPTION ALL-<=))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (11 11 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<=-MONOTONE))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(MAKE-DEPTH-ARRAY-AUX
 (301 301 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (250 54 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (217 69 (:REWRITE DEFAULT-<-2))
 (208 26 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (122 46 (:REWRITE DEFAULT-+-2))
 (104 26 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (80 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (69 69 (:REWRITE USE-ALL-<=-2))
 (69 69 (:REWRITE USE-ALL-<=))
 (69 69 (:REWRITE USE-ALL-<-2))
 (69 69 (:REWRITE USE-ALL-<))
 (69 69 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (56 14 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (53 53 (:REWRITE USE-ALL-RATIONALP-2))
 (53 53 (:REWRITE USE-ALL-RATIONALP))
 (52 52 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (48 36 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (48 36 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (46 46 (:REWRITE DEFAULT-+-1))
 (33 33 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (28 28 (:REWRITE USE-ALL-CONSP-2))
 (28 28 (:REWRITE USE-ALL-CONSP))
 (28 28 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (26 26 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (21 21 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (19 19 (:REWRITE USE-ALL-NATP-2))
 (19 19 (:REWRITE USE-ALL-NATP))
 (19 19 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (19 1 (:REWRITE ALL-DARGP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (11 11 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (11 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (8 5 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (8 4 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (2 1 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX-ALT))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-ALT))
 )
(ALEN1-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-AUX
 (649 649 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (234 117 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (72 9 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (69 35 (:REWRITE DEFAULT-+-2))
 (42 42 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (35 35 (:REWRITE DEFAULT-+-1))
 (32 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (29 23 (:REWRITE DEFAULT-<-2))
 (28 2 (:DEFINITION MAX))
 (25 23 (:REWRITE DEFAULT-<-1))
 (23 23 (:REWRITE USE-ALL-<=-2))
 (23 23 (:REWRITE USE-ALL-<=))
 (23 23 (:REWRITE USE-ALL-<-2))
 (23 23 (:REWRITE USE-ALL-<))
 (23 23 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
 (18 18 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE USE-ALL-CONSP-2))
 (10 10 (:REWRITE USE-ALL-CONSP))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (9 9 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (9 9 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (9 9 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (8 8 (:REWRITE USE-ALL-RATIONALP-2))
 (8 8 (:REWRITE USE-ALL-RATIONALP))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(ARRAY1P-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-AUX
 (647 647 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (234 117 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (72 9 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (62 33 (:REWRITE DEFAULT-+-2))
 (40 40 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (33 33 (:REWRITE DEFAULT-+-1))
 (29 23 (:REWRITE DEFAULT-<-2))
 (28 28 (:LINEAR ARRAY2P-LINEAR))
 (28 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (28 2 (:DEFINITION MAX))
 (25 23 (:REWRITE DEFAULT-<-1))
 (23 23 (:REWRITE USE-ALL-<=-2))
 (23 23 (:REWRITE USE-ALL-<=))
 (23 23 (:REWRITE USE-ALL-<-2))
 (23 23 (:REWRITE USE-ALL-<))
 (23 23 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (18 18 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE USE-ALL-CONSP-2))
 (10 10 (:REWRITE USE-ALL-CONSP))
 (10 10 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (9 9 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (9 9 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (9 9 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (7 7 (:REWRITE USE-ALL-RATIONALP-2))
 (7 7 (:REWRITE USE-ALL-RATIONALP))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(ALL-<-OF-+-OF-1-AND-MAXELEM-GEN
 (43547 279 (:REWRITE USE-ALL-<-FOR-CAR))
 (42945 107 (:DEFINITION NAT-LISTP))
 (35303 107 (:DEFINITION NATP))
 (32456 460 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (28045 89 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (27828 64 (:REWRITE INTEGER-LISTP-WHEN-ALL-NATP))
 (27702 327 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (21258 493 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (20706 30 (:REWRITE <-OF-+-AND-+-COMBINE-CONSTANTS))
 (20443 245 (:REWRITE ALL-<-OF-CDR))
 (18242 926 (:REWRITE DEFAULT-+-2))
 (16011 40 (:REWRITE ALL-<-OF-+-OF-1-AND-MAXELEM))
 (14438 776 (:REWRITE DEFAULT-<-2))
 (12592 288 (:LINEAR MAXELEM-OF-CDR-LINEAR))
 (7260 3630 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM))
 (6832 576 (:DEFINITION LEN))
 (6598 3630 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (4737 4737 (:TYPE-PRESCRIPTION ALL-NATP))
 (4721 180 (:REWRITE NOT-<-OF-MAXELEM-WHEN-ALL-<))
 (3304 776 (:REWRITE DEFAULT-<-1))
 (3192 3192 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (3120 172 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3117 3117 (:TYPE-PRESCRIPTION LEN))
 (2079 280 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (2018 2018 (:REWRITE DEFAULT-CDR))
 (1833 117 (:REWRITE ALL-NATP-OF-CDR))
 (1209 180 (:REWRITE NOT-<-OF-MAXELEM-WHEN-ALL-<-2))
 (1191 65 (:REWRITE RATIONALP-OF-MAXELEM))
 (1152 1152 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1152 1152 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1152 1152 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1080 1080 (:REWRITE USE-ALL-CONSP-2))
 (1080 1080 (:REWRITE USE-ALL-CONSP))
 (930 52 (:DEFINITION RATIONAL-LISTP))
 (926 926 (:REWRITE DEFAULT-+-1))
 (920 184 (:REWRITE NTH-OF-CDR))
 (876 455 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (814 776 (:REWRITE USE-ALL-<))
 (776 776 (:REWRITE USE-ALL-<-2))
 (776 776 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (758 5 (:REWRITE <-OF-MAXELEM-WHEN-ALL-<))
 (733 733 (:REWRITE DEFAULT-CAR))
 (723 107 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (690 106 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (654 327 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (612 280 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (557 279 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (523 523 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (474 237 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (460 460 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (449 327 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (402 30 (:REWRITE UNICITY-OF-0))
 (389 32 (:DEFINITION FIX))
 (384 150 (:REWRITE MAXELEM-BOUND-WHEN-ALL-<))
 (358 358 (:REWRITE USE-ALL-<=-2))
 (358 358 (:REWRITE USE-ALL-<=))
 (327 327 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (288 288 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (288 288 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (276 276 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (274 137 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (274 137 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (237 237 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (237 237 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (208 104 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (189 189 (:REWRITE USE-ALL-RATIONALP-2))
 (189 189 (:REWRITE USE-ALL-RATIONALP))
 (180 180 (:REWRITE LESS-THAN-MAXELEM-WHEN-LESS-THAN-SOME-ELEM))
 (160 32 (:REWRITE ALL-RATIONALP-OF-CDR))
 (149 149 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (138 138 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (138 138 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (137 137 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (137 137 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (137 137 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (134 134 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (128 128 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (107 107 (:REWRITE USE-ALL-NATP-2))
 (107 107 (:REWRITE USE-ALL-NATP))
 (107 107 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (71 53 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (47 5 (:REWRITE <=-OF-MAXELEM-WHEN-MEMBER-EQUAL))
 (38 38 (:TYPE-PRESCRIPTION MEMBERP))
 (35 2 (:REWRITE RATIONALP-OF-+-WHEN-RATIONALP-ARG1))
 (32 5 (:DEFINITION MEMBER-EQUAL))
 (30 30 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (25 25 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (25 2 (:REWRITE RATIONALP-OF-+-WHEN-RATIONALP-ARG2))
 (10 5 (:REWRITE <-OF-MAXELEM-WHEN-ALL-<-CHEAP))
 )
(DEPTH-ARRAYP-OF-ASET1-LIST
 (1076 43 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1044 14 (:DEFINITION NAT-LISTP))
 (197 29 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (154 16 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (145 145 (:TYPE-PRESCRIPTION NAT-LISTP))
 (105 21 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (100 52 (:REWRITE DEFAULT-<-2))
 (86 43 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (81 53 (:REWRITE USE-ALL-<))
 (56 29 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (55 52 (:REWRITE DEFAULT-<-1))
 (53 53 (:REWRITE USE-ALL-<-2))
 (53 53 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (53 39 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (52 52 (:REWRITE USE-ALL-<=-2))
 (52 52 (:REWRITE USE-ALL-<=))
 (51 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (44 44 (:TYPE-PRESCRIPTION MEMBERP))
 (39 25 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (37 21 (:REWRITE USE-ALL-NATP))
 (34 34 (:REWRITE USE-ALL-CONSP-2))
 (34 34 (:REWRITE USE-ALL-CONSP))
 (30 15 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (28 14 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (28 1 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (27 27 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE DEFAULT-CDR))
 (26 13 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (26 13 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (23 23 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (21 21 (:REWRITE USE-ALL-NATP-2))
 (21 21 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (17 17 (:REWRITE USE-ALL-RATIONALP-2))
 (17 17 (:REWRITE USE-ALL-RATIONALP))
 (16 16 (:LINEAR ARRAY2P-LINEAR))
 (13 13 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (13 13 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (13 13 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (12 12 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (12 12 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE USE-ALL-<=-FOR-CAR))
 (6 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1))
 (5 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:TYPE-PRESCRIPTION ALL-<=))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<=-MONOTONE))
 )
(MAKE-DEPTH-ARRAY-FOR-NODES
 (226 226 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (162 5 (:DEFINITION NAT-LISTP))
 (147 7 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (90 45 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (90 2 (:DEFINITION NATP))
 (83 83 (:TYPE-PRESCRIPTION NAT-LISTP))
 (54 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (22 3 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (21 5 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (20 3 (:REWRITE MAXELEM-BOUND-MAXINT))
 (19 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (18 3 (:REWRITE ALL-<-TRANSITIVE))
 (18 2 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (16 4 (:REWRITE DEFAULT-+-2))
 (14 7 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (12 10 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (11 11 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (11 5 (:REWRITE USE-ALL-NATP))
 (10 10 (:TYPE-PRESCRIPTION MEMBERP))
 (10 6 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE USE-ALL-<=-2))
 (6 6 (:REWRITE USE-ALL-<=))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (5 5 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (4 1 (:REWRITE MAXELEM-SINGLETON-ALT))
 (3 3 (:REWRITE USE-ALL-CONSP-2))
 (3 3 (:REWRITE USE-ALL-CONSP))
 (3 3 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (3 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (1 1 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 )
(ALEN1-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-FOR-NODES
 (95 3 (:DEFINITION NAT-LISTP))
 (94 47 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (74 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (68 68 (:TYPE-PRESCRIPTION NAT-LISTP))
 (53 1 (:DEFINITION NATP))
 (35 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (19 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (18 1 (:REWRITE MAXELEM-BOUND-MAXINT))
 (16 4 (:REWRITE MAXELEM-SINGLETON-ALT))
 (12 3 (:REWRITE DEFAULT-+-2))
 (11 3 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (11 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (9 2 (:REWRITE ALL-<-TRANSITIVE))
 (9 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 3 (:REWRITE USE-ALL-NATP))
 (6 6 (:TYPE-PRESCRIPTION MEMBERP))
 (6 4 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (6 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (5 5 (:REWRITE USE-ALL-CONSP-2))
 (5 5 (:REWRITE USE-ALL-CONSP))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (5 3 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (3 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (2 2 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 1 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (1 1 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (1 1 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(ARRAY1P-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-FOR-NODES
 (95 3 (:DEFINITION NAT-LISTP))
 (74 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (53 1 (:DEFINITION NATP))
 (35 35 (:TYPE-PRESCRIPTION NAT-LISTP))
 (35 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (28 14 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (19 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (18 1 (:REWRITE MAXELEM-BOUND-MAXINT))
 (12 3 (:REWRITE MAXELEM-SINGLETON-ALT))
 (11 3 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (11 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (9 2 (:REWRITE ALL-<-TRANSITIVE))
 (9 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (8 2 (:REWRITE DEFAULT-+-2))
 (7 3 (:REWRITE USE-ALL-NATP))
 (6 6 (:TYPE-PRESCRIPTION MEMBERP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (5 3 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE USE-ALL-CONSP-2))
 (4 4 (:REWRITE USE-ALL-CONSP))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (3 3 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (3 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 1 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (1 1 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (1 1 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
