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|
(th_E
(fac_TCC1 0
(fac_TCC1-1 nil 3667132061 ("" (subtype-tcc) nil nil) nil nil))
(fac_TCC2 0
(fac_TCC2-1 nil 3667132061 ("" (termination-tcc) nil nil) nil nil))
(thm_E_0 0
(thm_E_0-1 nil 3667136110
("" (induct k)
(("1" (flatten) (("1" (assert) nil nil)) nil)
("2" (skeep)
(("2" (split -1)
(("1" (expand fac 1 2) (("1" (assert) nil nil)) nil)
("2" (case "j=0")
(("1" (expand fac 2)
(("1" (expand fac 2)
(("1" (assert 2)
(("1" (expand fac 2)
(("1" (assert 2) (("1" (grind 2) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
((= const-decl "[T, T -> boolean]" equalities nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nat_induction formula-decl nil naturalnumbers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(fac def-decl "nat" th_E nil) (< const-decl "bool" reals nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil))
shostak))
(thm_E_1 0
(thm_E_1-1 nil 3667132062
("" (induct k)
(("1" (assert) (("1" (grind) nil nil)) nil)
("2" (skeep) (("2" (expand fac 1) (("2" (assert) nil nil)) nil))
nil))
nil)
((mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nat_induction formula-decl nil naturalnumbers nil)
(fac def-decl "nat" th_E nil) (<= const-decl "bool" reals nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(thm_E_2 0
(thm_E_2-1 nil 3667133505
("" (induct k)
(("1" (expand fac) (("1" (assert) nil nil)) nil)
("2" (skeep)
(("2" (lemma thm_E_0)
(("2" (inst -1 j)
(("2" (split -1)
(("1" (assert) nil nil)
("2" (assert)
(("2" (case "j=0")
(("1" (expand fac 2)
(("1" (expand fac 2) (("1" (assert 2) nil nil)) nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(thm_E_0 formula-decl nil th_E nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nat_induction formula-decl nil naturalnumbers nil)
(fac def-decl "nat" th_E nil) (<= const-decl "bool" reals nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(tfac_TCC1 0
(tfac_TCC1-1 nil 3667133493 ("" (subtype-tcc) nil nil) nil nil))
(tfac_TCC2 0
(tfac_TCC2-1 nil 3667133493 ("" (termination-tcc) nil nil) nil nil))
(lemma_E_3 0
(lemma_E_3-1 nil 3667135000
("" (induct m)
(("1" (skeep)
(("1" (expand tfac)
(("1" (expand fac) (("1" (propax) nil nil)) nil)) nil))
nil)
("2" (skeep)
(("2" (skeep 1)
(("2" (expand tfac 1)
(("2" (inst -1 "j*n+n")
(("2" (replace -1 1)
(("2" (expand fac 1 2) (("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(fac def-decl "nat" th_E nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(tfac def-decl "nat" th_E nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(th_E_4 0
(th_E_4-1 nil 3667136822
("" (skeep)
(("" (lemma lemma_E_3)
(("" (inst -1 k 1) (("" (assert) nil nil)) nil)) nil))
nil)
((lemma_E_3 formula-decl nil th_E nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(fib_TCC1 0
(fib_TCC1-1 nil 3667132061 ("" (subtype-tcc) nil nil) nil nil))
(fib_TCC2 0
(fib_TCC2-1 nil 3667132061 ("" (termination-tcc) nil nil) nil nil))
(lem_E_Camil_1 0
(lem_E_Camil_1-1 nil 3667137364
("" (induct i)
(("1" (skeep)
(("1" (expand tfib)
(("1" (expand fib) (("1" (propax) nil nil)) nil)) nil))
nil)
("2" (skeep)
(("2" (skeep 1)
(("2" (expand tfib 1) (("2" (postpone) nil nil)) nil)) nil))
nil))
nil)
nil shostak))
(lem_E_Camil_2_TCC1 0
(lem_E_Camil_2_TCC1-1 nil 3667140798 ("" (subtype-tcc) nil nil) nil
nil))
(lem_E_Camil_2_TCC2 0
(lem_E_Camil_2_TCC2-1 nil 3667140798 ("" (subtype-tcc) nil nil) nil
nil))
(lem_E_Camil_2 0
(lem_E_Camil_2-1 nil 3667137463
("" (induct i)
(("1" (skeep) (("1" (expand tfib) (("1" (propax) nil nil)) nil))
nil)
("2" (skeep)
(("2" (skeep 1)
(("2" (case "j=0")
(("1" (assert)
(("1" (expand tfib)
(("1" (expand tfib) (("1" (propax) nil nil)) nil)) nil))
nil)
("2" (assert 2)
(("2" (expand tfib 2)
(("2" (inst -1 p (m+p))
(("2" (replace -1 2)
(("2" (case "j=1")
(("1" (assert)
(("1" (expand fib 2) (("1" (assert) nil nil))
nil))
nil)
("2" (assert 3)
(("2" (lift-if)
(("2" (assert)
(("2" (expand fib 3 3)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skeep 1) (("3" (assert) nil nil)) nil)
("4" (skeep 1) (("4" (assert) nil nil)) nil))
nil)
((real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(fib def-decl "nat" th_E nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(tfib def-decl "nat" th_E nil)
(pred type-eq-decl nil defined_types nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(int_minus_int_is_int application-judgement "int" integers nil))
shostak))
(thm_E_6 0
(thm_E_6-1 nil 3667137014
("" (skeep)
(("" (lemma lem_E_Camil_2)
(("" (inst -1 i 1 1)
(("" (assert)
(("" (replace -1 1)
(("" (assert)
(("" (case "i=0")
(("1" (assert)
(("1" (expand fib 1) (("1" (propax) nil nil)) nil))
nil)
("2" (case "i=1")
(("1" (assert)
(("1" (expand fib 2) (("1" (propax) nil nil)) nil))
nil)
("2" (assert)
(("2" (expand fib 3 3) (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((lem_E_Camil_2 formula-decl nil th_E nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(fib def-decl "nat" th_E nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak)))
|
