(max_below
(max_TCC1 0
(max_TCC1-1 nil 3276608569
("" (inst 1 "(LAMBDA S: N-1 - min({y: below[N] | S(N-1-y)}))")
(("1" (skosimp*)
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(("1" (ground)
(("1" (skosimp*)
(("1" (inst - "N-1-x!1") (("1" (assert) nil nil)) nil))
nil))
nil)
("2" (hide 2)
(("2" (expand "nonempty?")
(("2" (typepred "S!1")
(("2" (expand "nonempty?")
(("2" (expand "empty?")
(("2" (skosimp*)
(("2" (expand "member")
(("2" (inst -2 "N-1-x!1")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (typepred "S!1")
(("2" (expand "nonempty?")
(("2" (expand "empty?")
(("2" (skosimp*)
(("2" (expand "member")
(("2" (inst - "N-1-x!1") (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(real_lt_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)
(NOT const-decl "[bool -> bool]" booleans nil)
(min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
min_nat nil)
(<= const-decl "bool" reals nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nonempty? const-decl "bool" sets nil)
(set type-eq-decl nil sets nil)
(below type-eq-decl nil nat_types nil)
(N formal-const-decl "nat" max_below nil)
(< const-decl "bool" reals 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)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(max_def 0
(max_def-1 nil 3276608569
("" (skolem-typepred)
(("" (typepred "max(S!1)")
(("" (prop)
(("1" (expand "maximum?")
(("1" (assert)
(("1" (skosimp*)
(("1" (inst?) (("1" (assert) nil nil)) nil)) nil))
nil))
nil)
("2" (expand "maximum?")
(("2" (flatten)
(("2" (inst -5 "a!1")
(("2" (assert)
(("2" (inst -2 "max(S!1)") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((max const-decl
"{a: below[N] | S(a) AND (FORALL x: S(x) IMPLIES a >= x)}"
max_below nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(maximum? const-decl "bool" max_below 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)
(nonempty? const-decl "bool" sets nil)
(set type-eq-decl nil sets nil)
(below type-eq-decl nil nat_types nil)
(N formal-const-decl "nat" max_below nil)
(< const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(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))
nil))
(max_lem 0
(max_lem-1 nil 3276608569
("" (skosimp*)
(("" (expand "maximum?")
(("" (assert)
(("" (lemma "max_def")
(("" (inst?) (("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((maximum? const-decl "bool" max_below nil)
(max_def formula-decl nil max_below nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(max const-decl
"{a: below[N] | S(a) AND (FORALL x: S(x) IMPLIES a >= x)}"
max_below nil)
(nonempty? const-decl "bool" sets nil)
(set type-eq-decl nil sets nil)
(below type-eq-decl nil nat_types nil)
(N formal-const-decl "nat" max_below nil)
(< const-decl "bool" reals 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))
nil)))
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