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|
(th_D
(sum_TCC1 0
(sum_TCC1-1 nil 3667129223 ("" (subtype-tcc) nil nil) nil nil))
(sum_TCC2 0
(sum_TCC2-1 nil 3667129223 ("" (termination-tcc) nil nil) nil nil))
(D_1 0
(D_1-1 nil 3667129225
("" (induct n)
(("1" (assert) (("1" (grind) nil nil)) nil)
("2" (skeep) (("2" (expand sum 1) (("2" (assert) nil nil)) nil))
nil))
nil)
((nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_plus_odd_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
nil
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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))
(D_2 0
(D_2-1 nil 3667129345
("" (induct n)
(("1" (grind) nil nil)
("2" (skeep)
(("2" (expand sum 1)
(("2" (expand id 1 1) (("2" (grind) nil nil)) nil)) nil))
nil))
nil)
((nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(id_preserves application-judgement "S" identity_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(even_plus_odd_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(id const-decl "(bijective?[T, T])" identity nil)
(bijective? const-decl "bool" functions nil) nil
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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))
(pow_TCC1 0
(pow_TCC1-1 nil 3667129223 ("" (skeep) (("" (assert) nil nil)) nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(pow_TCC2 0
(pow_TCC2-1 nil 3667144387 ("" (termination-tcc) nil nil) nil nil)))
(th_Da
(Da_1 0
(Da_1-1 nil 3667129545
("" (induct n1)
(("1" (expand sum)
(("1" (expand square) (("1" (propax) nil nil)) nil)) nil)
("2" (skeep)
(("2" (expand sum 1)
(("2" (replace -1 1)
(("2" (assert) (("2" (grind) nil nil)) nil)) nil))
nil))
nil))
nil)
((posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(square const-decl "nat" th_Da nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil) 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)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(even_plus_odd_is_odd application-judgement "odd_int" integers
nil))
shostak))
(Da_2 0
(Da_2-1 nil 3667129831
("" (induct n)
(("1" (grind) nil nil)
("2" (skeep)
(("2" (expand sum 1)
(("2" (replace -1 1) (("2" (grind) nil nil)) nil)) nil))
nil))
nil)
((posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(even_plus_even_is_even application-judgement "even_int" integers
nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(even_plus_odd_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(square const-decl "nat" th_Da nil) nil
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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))
(Da_3 0
(Da_3-1 nil 3667129862
("" (induct n)
(("1" (grind) nil nil)
("2" (skeep)
(("2" (expand sum 1 1)
(("2" (expand sum 1 2)
(("2" (replace -1 1)
(("2" (expand square 1)
(("2" (expand cube 1)
(("2" (lemma D_1)
(("2" (inst -1 j)
(("2" (replace -1 1) (("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((mult_divides2 application-judgement "(divides(m))" divides nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(D_1 formula-decl nil th_D nil)
(even_plus_even_is_even application-judgement "even_int" integers
nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil) nil
(square const-decl "nat" th_Da nil)
(cube const-decl "nat" th_Da nil) 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))
(Da_4 0
(Da_4-1 nil 3667130517
("" (induct n1)
(("1" (grind) nil nil)
("2" (skeep)
(("2" (expand sum 1)
(("2" (replace -1 1)
(("2" (expand pow 1 3) (("2" (propax) nil nil)) nil)) nil))
nil))
nil))
nil)
((nnint_plus_posint_is_posint application-judgement "posint"
integers 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)
(pred type-eq-decl nil defined_types nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(sum def-decl "nat" th_D nil) (pow def-decl "nat" th_D nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nat_induction formula-decl nil naturalnumbers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(even_plus_odd_is_odd application-judgement "odd_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)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil))
shostak))
(Da_5 0
(Da_5-1 nil 3667130601
("" (induct n1)
(("1" (expand sum 1) (("1" (propax) nil nil)) nil)
("2" (skeep) (("2" (expand sum 1) (("2" (propax) nil nil)) nil))
nil))
nil)
((nat_induction formula-decl nil naturalnumbers nil) nil
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(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))
shostak)))
(th_Db
(geom_TCC1 0
(geom_TCC1-1 nil 3667129224 ("" (subtype-tcc) nil nil) nil nil))
(geom_TCC2 0
(geom_TCC2-1 nil 3667129224 ("" (subtype-tcc) nil nil) nil nil))
(geom_TCC3 0
(geom_TCC3-1 nil 3667129224 ("" (termination-tcc) nil nil) nil nil))
(geom_sum 0
(geom_sum-1 nil 3667130791
("" (induct a)
(("1" (induct n)
(("1" (grind) nil nil)
("2" (skeep)
(("2" (split -1)
(("1" (expand geom 1)
(("1" (replace -1 1) (("1" (grind) nil nil)) nil)) nil)
("2" (propax) nil nil))
nil))
nil))
nil)
("2" (skeep)
(("2" (induct n)
(("1" (grind) nil nil)
("2" (skolem 1 k)
(("2" (flatten 1)
(("2" (split -1)
(("1" (expand geom 1)
(("1" (replace -1 1)
(("1" (expand pow 1 3) (("1" (propax) nil nil)) nil))
nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(nzint_times_nzint_is_nzint application-judgement "nzint" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(pow def-decl "nat" th_D nil) (geom def-decl "posnat" th_Db nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(= const-decl "[T, T -> boolean]" equalities 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))
shostak)))
|
