|
(remx
(modx_TCC1 0
(modx_TCC1-1 nil 3412912493
("" (skosimp)
(("" (typepred "floor(n!1 / b!1)")
(("" (name-replace "N" "floor(n!1 / b!1)")
(("" (rewrite "div_mult_pos_le2")
(("" (rewrite "div_mult_pos_lt1") (("" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
((posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(integer nonempty-type-from-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)
(<= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(div_mult_pos_le2 formula-decl nil real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props 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)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(div_mult_pos_lt1 formula-decl nil real_props 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 "[T, T -> boolean]" equalities nil))
nil))
(modx_def 0
(modx_def-1 nil 3412912600
("" (skosimp)
(("" (expand "modx")
(("" (lemma "rem_floor" ("b" "b!1" "x" "n!1"))
(("" (assert) nil nil)) nil))
nil))
nil)
((nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(modx const-decl "below[b]" remx nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(rem_floor formula-decl nil modulo_arithmetic 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)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil))
shostak))
(remx_TCC1 0
(remx_TCC1-1 nil 3412912493
("" (skosimp)
((""
(lemma "both_sides_times_neg_le1"
("nz" "i!1" "y" "0" "x" "b!1-1"))
(("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
nil)
((posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(>= const-decl "bool" reals nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(both_sides_times_neg_le1 formula-decl nil real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil))
nil))
(remx_def 0
(remx_def-1 nil 3412913517
("" (expand "remx")
(("" (skosimp)
(("" (case-replace "i!1>=0")
(("1" (rewrite "modx_def") nil nil)
("2" (assert)
(("2"
(lemma "both_sides_times_neg_le1"
("nz" "i!1" "y" "0" "x" "b!1-1"))
(("2" (assert)
(("2" (rewrite "modx_def")
(("2" (rewrite "same_remainder")
(("2" (expand "divides")
(("2" (inst + "-i!1") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(same_remainder formula-decl nil modulo_arithmetic nil)
(minus_int_is_int application-judgement "int" integers nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(divides const-decl "bool" divides nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(both_sides_times_neg_le1 formula-decl nil real_props nil)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(modx_def formula-decl nil remx nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(remx const-decl "below[b]" remx nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil))
shostak)))
¤ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
¤
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