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(expt_inv_left formula-decl nil group nil)
(assoc formula-decl nil group nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil)
(i!1 skolem-const-decl "int" cyclic_group nil)
(q!1 skolem-const-decl "int" cyclic_group nil)
(restrict const-decl "R" restrict nil)
(commutative? const-decl "bool" operator_defs nil)
(abelian_group? const-decl "bool" group_def nil)
(cyclic_abelian formula-decl nil cyclic_group nil)
(mod nonempty-type-eq-decl nil euclidean_division nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(subset? const-decl "bool" sets nil)
(min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
min_nat nil)
(<= const-decl "bool" reals nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(nonempty? const-decl "bool" sets 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)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil))
shostak))
(is_cyclic 0
(is_cyclic-1 nil 3407083622
("" (skosimp*)
(("" (expand "cyclic?")
(("" (inst + "a!1")
(("" (apply-extensionality 1 :hide? t)
(("" (iff 1)
(("" (inst?)
(("1" (skosimp*)
(("1" (replace -1)
(("1" (hide -1)
(("1" (ground)
(("1" (expand "generated_by")
(("1" (inst?) nil nil)) nil)
("2" (lemma "generated_is_subgroup")
(("2" (inst?)
(("2" (assert)
(("2" (inst - "G!1")
(("2"
(assert)
(("2"
(expand "subgroup?")
(("2"
(expand "subset?")
(("2"
(inst - "a!1 ^ n!1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2" (lemma "generated_is_subgroup")
(("2" (inst - "G!1" "a!1")
(("2" (assert)
(("2" (expand "subgroup?")
(("2" (expand "subset?")
(("2" (inst?) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cyclic? const-decl "boolean" group nil)
(generated_by const-decl "group" group nil)
(x!1 skolem-const-decl "T" cyclic_group nil)
(G!1 skolem-const-decl "group[T, *, one]" cyclic_group 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)
(subgroup? const-decl "bool" group_def nil)
(^ const-decl "T" group nil) (subset? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(generated_is_subgroup formula-decl nil cyclic_group nil)
(group nonempty-type-eq-decl nil group nil)
(group? const-decl "bool" group_def nil)
(one formal-const-decl "T" cyclic_group nil)
(* formal-const-decl "[T, T -> T]" cyclic_group nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(T formal-nonempty-type-decl nil cyclic_group nil))
nil)))
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