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nil)
(div const-decl "integer" div nil)
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
real_defs nil)
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("" (skosimp*)
(("" (expand "div")
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(inst
-1
"abs(j!1)"
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nil))
nil))
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nil))
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nil))
nil))
nil))
nil))
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(div const-decl "integer" div nil)
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(minus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
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(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
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(mult_divides1 application-judgement "(divides(n))" divides nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(both_sides_times_pos_lt1 formula-decl nil real_props nil)
(abs_nat_rew formula-decl nil abs_rews nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(posint_times_posint_is_posint application-judgement "posint"
integers nil)
(nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
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integers nil)
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(> const-decl "bool" reals nil)
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(("" (case "i!1 = 0")
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nil)
("2" (expand "div")
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nil))
nil))
nil)
((int nonempty-type-eq-decl nil integers nil)
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(div_zero formula-decl nil div nil)
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(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
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(mult_divides1 application-judgement "(divides(n))" divides nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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"(strict_total_order?[real])" real_props nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
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(integer nonempty-type-from-decl nil integers nil)
(div const-decl "integer" div nil)
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
real_defs nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil))
nil))
(div_lt_nat 0
(div_lt_nat-1 nil 3407841515
("" (skosimp*)
(("" (lemma "div_lt")
(("" (inst?) (("" (expand "abs") (("" (assert) nil nil)) nil))
nil))
nil))
nil)
((div_lt formula-decl nil div nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(/= const-decl "boolean" notequal nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
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(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))
nil))
(div_is_0 0
(div_is_0-1 nil 3407841515
("" (skosimp*)
(("" (lemma "div_eq_0")
(("" (inst?)
(("" (lemma "div_lt")
(("" (inst?) (("" (ground) nil nil)) nil)) nil))
nil))
nil))
nil)
((div_eq_0 formula-decl nil div nil)
(div_lt formula-decl nil div nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(/= const-decl "boolean" notequal nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
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(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
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(boolean nonempty-type-decl nil booleans nil)
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nil))
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(div_parity-1 nil 3407841515
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(("" (expand "div")
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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real_defs nil)
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
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nil)
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(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
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)
(/= const-decl "boolean" notequal nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(sgn const-decl "int" real_defs nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(abs_nat_rew formula-decl nil abs_rews nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(both_sides_div_pos_le1 formula-decl nil real_props nil))
nil))
(div_parity_neg 0
(div_parity_neg-1 nil 3407841515
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(("" (expand "div")
(("" (lemma "both_sides_div_pos_le1")
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
real_defs nil)
(div const-decl "integer" div nil)
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nil)
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(> const-decl "bool" reals nil)
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(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
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(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(/= const-decl "boolean" notequal nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(sgn const-decl "int" real_defs nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(abs_nat_rew formula-decl nil abs_rews nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_ge_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)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(both_sides_div_pos_le1 formula-decl nil real_props nil))
nil))
(div_ge_0 0
(div_ge_0-1 nil 3407841515
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(("" (lemma "div_parity")
(("" (inst?)
(("" (lemma "div_is_0")
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(("" (lemma "div_parity_neg")
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nil))
nil))
nil))
nil))
nil)
((div_parity formula-decl nil div nil)
(div_is_0 formula-decl nil div nil)
(div_parity_neg formula-decl nil div nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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real_defs nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(/= const-decl "boolean" notequal nil)
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(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))
nil))
(div_le_0 0
(div_le_0-1 nil 3407841515
("" (skosimp*)
(("" (lemma "div_parity")
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(("" (lemma "div_is_0")
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(("" (lemma "div_parity_neg")
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nil))
nil))
nil))
nil))
nil)
((div_parity formula-decl nil div nil)
(div_is_0 formula-decl nil div nil)
(div_parity_neg formula-decl nil div nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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real_defs nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(real_gt_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)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(/= const-decl "boolean" notequal 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))
nil))
(div_smaller 0
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("" (skosimp*)
(("" (expand "div")
(("" (expand "sgn")
(("" (expand "abs")
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(("" (flatten) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
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real_defs nil)
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nil)
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(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)
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(+ 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)
(posreal nonempty-type-eq-decl nil real_types nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
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rationals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(both_sides_times_pos_le1 formula-decl nil real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
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)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(sgn const-decl "int" real_defs nil))
nil))
(div_abs 0
(div_abs-1 nil 3407841515
("" (skosimp*)
(("" (grind)
(("1" (lemma "pos_div_ge")
(("1" (inst?) (("1" (assert) nil nil)) nil)) nil)
("2" (lemma "pos_div_ge")
(("2" (inst?) (("2" (assert) nil nil)) nil)) nil)
("3" (lemma "pos_div_ge")
(("3" (inst?) (("3" (assert) nil nil)) nil)) nil)
("4" (lemma "pos_div_ge")
(("4" (inst?) (("4" (assert) nil nil)) nil)) nil))
nil))
nil)
((div const-decl "integer" div nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
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real_defs nil)
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real_defs nil)
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(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(minus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(nonzero_integer nonempty-type-eq-decl nil integers 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 "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal 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)
(pos_div_ge formula-decl nil real_props nil))
nil))
(div_max 0
(div_max-1 nil 3407841515
("" (skosimp*)
(("" (lemma "div_smaller")
(("" (lemma "div_abs")
(("" (inst?)
(("" (replace -1) (("" (hide -1) (("" (inst?) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((div_smaller formula-decl nil div 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)
(/= const-decl "boolean" notequal nil)
(nonzero_integer 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)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
real_defs nil)
(div_abs formula-decl nil div nil))
nil))
(div_multiple 0
(div_multiple-1 nil 3407841515
("" (skosimp*) (("" (rewrite "div_def") (("" (grind) nil nil)) nil))
nil)
((mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(div_def formula-decl nil div 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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/= const-decl "boolean" notequal nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(div_even 0
(div_even-1 nil 3407841515
("" (skosimp*)
(("" (lemma "div_multiple")
(("" (case "(EXISTS k: j!1*k = i!1)")
(("1" (skosimp*)
(("1" (inst -2 "j!1" "k!1") (("1" (assert) nil nil)) nil))
nil)
("2" (inst 1 "i!1/j!1") (("2" (assert) nil nil)) nil))
nil))
nil))
nil)
((div_multiple formula-decl nil div nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(i!1 skolem-const-decl "int" div nil)
(j!1 skolem-const-decl "nonzero_integer" div nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides 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)
(= const-decl "[T, T -> boolean]" equalities nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/= const-decl "boolean" notequal nil)
(nonzero_integer nonempty-type-eq-decl nil integers nil))
nil))
(div_sum 0
(div_sum-1 nil 3407841515
("" (skosimp*)
(("" (expand "div")
(("" (expand "abs")
(("" (lift-if)
(("" (expand "sgn")
(("" (lift-if)
(("" (assert)
(("" (lift-if)
(("" (lift-if)
(("" (lemma "floor_plus_int")
(("" (inst -1 "k!1" "i!1/j!1")
(("" (lemma "floor_neg")
(("" (inst -1 "i!1/j!1")
(("" (lemma "floor_plus_int")
((""
(inst -1 "-k!1" "-i!1/j!1")
((""
(lift-if)
((""
(expand "integer?")
((""
(split +)
(("1"
(flatten)
(("1"
(lift-if)
(("1"
(lift-if)
(("1"
(ground)
(("1"
(lift-if)
(("1"
(ground)
(("1"
(lift-if)
(("1"
(ground)
nil
nil))
nil)
("2"
(lift-if)
(("2"
(ground)
nil
nil))
nil))
nil))
nil)
("2"
(lift-if)
(("2"
(ground)
nil
nil))
nil)
("3"
(lift-if)
(("3"
(ground)
nil
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(ground)
(("2"
(lift-if)
(("2"
(ground)
(("1"
(lift-if)
(("1" (ground) nil nil))
nil)
("2"
(ground)
(("2"
(lift-if)
(("2"
(ground)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
real_defs nil)
(nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
real_defs nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(div const-decl "integer" div nil)
(floor_plus_int formula-decl nil floor_ceil nil)
(floor_neg formula-decl nil floor_ceil nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(minus_rat_is_rat application-judgement "rat" rationals nil)
(rat_plus_rat_is_rat application-judgement "rat" rationals nil)
(odd_times_odd_is_odd application-judgement "odd_int" integers nil)
(integer? const-decl "bool" integers nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(nonzero_integer 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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(int nonempty-type-eq-decl nil integers 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)
(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)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sgn const-decl "int" real_defs nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil)
(minus_int_is_int application-judgement "int" integers nil))
nil))
(div_sum_nat 0
(div_sum_nat-1 nil 3407841515
("" (skosimp*)
(("" (lemma "div_sum")
(("" (inst?)
(("" (expand "sgn")
(("" (lift-if) (("" (ground) nil nil)) nil)) nil))
nil))
nil))
nil)
((div_sum formula-decl nil div nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(sgn const-decl "int" real_defs nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.84 Sekunden
(vorverarbeitet)
¤
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