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nil))
nil))
nil))
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nil))
nil))
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(succ const-decl "subchain" zorn nil)
(add const-decl "(nonempty?)" sets nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
zorn nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(finite_emptyset name-judgement "finite_set[T]" zorn nil)
(T0_comparable? const-decl "bool" zorn nil)
(T0 const-decl "(tower?)" zorn nil)
(tower? const-decl "bool" zorn nil)
(subchain nonempty-type-eq-decl nil chain_chain nil)
(chain? const-decl "bool" chain nil)
(<= formal-const-decl "(partial_order?[T])" zorn nil)
(partial_order? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types nil)
(set type-eq-decl nil sets nil) (T formal-type-decl nil zorn nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(T0_all_comparable 0
(T0_all_comparable-1 nil 3314758046
("" (skolem!)
(("" (lemma "T0_smallest")
(("" (inst - "{ch: (T0_comparable?) | TRUE}")
(("1" (expand* "extend" "subset?" "member")
(("1" (inst - "ch!1") (("1" (assert) nil nil)) nil)) nil)
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(("2" (expand "tower?")
(("2" (prop)
(("1" (expand* "extend" "member")
(("1" (prop)
(("1" (expand "T0_comparable?")
(("1" (skosimp)
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nil))
nil))
nil))
nil))
nil)
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(("2" (prop)
(("1" (inst - "ch!2") nil nil)
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(("1" (assert) nil nil) ("2" (propax) nil nil))
nil))
nil))
nil))
nil)
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(("3" (expand* "extend" "member")
(("3" (prop)
(("1" (inst -5 "CH!1")
(("1" (assert)
(("1" (skolem!)
(("1" (inst - "ch!2")
(("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (expand "T0_comparable?" 1)
(("2" (skosimp)
(("2"
(expand* "chain_union" "subset?" "member"
"Union")
(("2" (skosimp* t)
(("2" (expand "extend")
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(prop)
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(("2"
(prop)
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(expand "T0_comparable?" -)
(("2"
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(expand* "subset?" "member")
(("2"
(split)
(("1"
(inst - "x!1")
(("1"
(inst + "a!1")
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(assert)
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nil))
nil))
nil)
("2"
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(assert)
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nil))
nil))
nil))
nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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((T0_smallest formula-decl nil zorn nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(emptyset const-decl "set" sets nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(finite_emptyset name-judgement "finite_set[T]" zorn nil)
(T0_comparable judgement-tcc nil zorn nil)
(Union const-decl "set" sets nil)
(chain_union const-decl "subchain" chain_chain nil)
(CH!1 skolem-const-decl "chain_chain[T, <=]" zorn nil)
(a!1 skolem-const-decl
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(chain_chain nonempty-type-eq-decl nil chain_chain nil)
(chain_incl const-decl "bool" chain_chain nil)
(subset? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(T formal-type-decl nil zorn nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(pred type-eq-decl nil defined_types nil)
(partial_order? const-decl "bool" orders nil)
(<= formal-const-decl "(partial_order?[T])" zorn nil)
(chain? const-decl "bool" chain nil)
(subchain nonempty-type-eq-decl nil chain_chain nil)
(tower? const-decl "bool" zorn nil)
(T0 const-decl "(tower?)" zorn nil)
(T0_comparable? const-decl "bool" zorn nil)
(FALSE const-decl "bool" booleans nil)
(extend const-decl "R" extend nil)
(TRUE const-decl "bool" booleans nil))
shostak))
(T0_chain 0
(T0_chain-1 nil 3314731120
("" (typepred "chain_incl")
((""
(expand* "chain?" "total_order?" "partial_order?" "preorder?"
"dichotomous?" "restrict")
(("" (skosimp)
(("" (lemma "T0_all_comparable" ("ch" "x!1"))
(("" (expand* "T0_comparable?" "chain_incl")
(("" (inst - "y!1") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((total_order? const-decl "bool" orders nil)
(preorder? const-decl "bool" orders nil)
(restrict const-decl "R" restrict nil)
(dichotomous? const-decl "bool" orders nil)
(partial_order_restrict application-judgement "(partial_order?[S])"
restrict_order_props nil)
(preorder_restrict application-judgement "(preorder?[S])"
restrict_order_props nil)
(transitive_restrict application-judgement "(transitive?[S])"
restrict_order_props nil)
(antisymmetric_restrict application-judgement "(antisymmetric?[S])"
restrict_order_props nil)
(reflexive_restrict application-judgement "(reflexive?[S])"
restrict_order_props nil)
(T0_all_comparable formula-decl nil zorn nil)
(tower? const-decl "bool" zorn nil)
(T0 const-decl "(tower?)" zorn nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
zorn nil)
(T0_comparable? const-decl "bool" zorn nil)
(chain_incl_partial_order name-judgement
"(partial_order?[subchain])" zorn nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(T formal-type-decl nil zorn nil) (set type-eq-decl nil sets nil)
(pred type-eq-decl nil defined_types nil)
(partial_order? const-decl "bool" orders nil)
(<= formal-const-decl "(partial_order?[T])" zorn nil)
(chain? const-decl "bool" chain nil)
(subchain nonempty-type-eq-decl nil chain_chain nil)
(chain_incl const-decl "bool" chain_chain nil))
nil))
(zorn 0
(zorn-1 nil 3314758540
("" (flatten)
(("" (lemma "maximal_chain_add_set" ("ch" "chain_union(T0)"))
(("" (prop)
(("1" (forward-chain "bounded_chain_upto")
(("1" (expand* "fullset" "maximal?" "member")
(("1" (inst - "chain_union(T0)")
(("1" (skolem!)
(("1" (use "maximal_upto_subset")
(("1" (inst 2 "t!1")
(("1" (prop)
(("1" (skosimp)
(("1" (inst - "r!1")
(("1" (assert)
(("1" (expand* "upto" "subset?" "member")
(("1"
(skosimp)
(("1"
(expand*
"fullset"
"maximal?"
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"union"
"member")
(("1"
(inst + "x!1")
(("1"
(assert)
(("1"
(typepred "<=")
(("1"
(expand*
"partial_order?"
"preorder?"
"transitive?")
(("1"
(flatten)
(("1"
(inst
-
"x!1"
"t!1"
"r!1")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
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nil))
nil))
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nil))
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(expand* "upto" "chain_incl" "subset?"
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(skosimp)
(("1"
(expand* "add" "member")
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nil))
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(decompose-equality)
(("2"
(inst - "r!1")
(("2"
(expand*
"add"
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"member")
(("2"
(inst - "t!1")
(("2"
(inst - "r!1")
(("2"
(typepred "<=")
(("2"
(expand*
"partial_order?"
"preorder?"
"antisymmetric?")
(("2"
(flatten)
(("2"
(inst - "t!1" "r!1")
(("2"
(ground)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "chain_union(T0)")
(("2"
(typepred "<=")
(("2"
(expand*
"chain?"
"total_order?"
"partial_order?"
"preorder?"
"restrict"
"dichotomous?")
(("2"
(skosimp :preds? t)
(("2"
(expand*
"add"
"reflexive?"
"reflexive_closure"
"union"
"member")
(("2"
(ground)
(("1"
(inst - "r!1")
(("1" (assert) nil nil))
nil)
("2"
(inst - "y!1")
(("2"
(inst - "y!1")
(("2"
(inst - "y!1")
(("2" (assert) nil nil))
nil))
nil))
nil)
("3"
(inst - "x!1")
(("3"
(inst - "x!1")
(("3"
(inst - "x!1")
(("3" (assert) nil nil))
nil))
nil))
nil)
("4"
(inst - "x!1" "y!1")
(("4" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand* "fullset" "maximal?" "member" "chain_incl")
(("2" (skosimp :preds? t)
(("2" (lemma "empty_succ" ("ch" "chain_union(T0)"))
(("2" (assert)
(("2" (apply-extensionality :hide? t)
(("2" (expand* "succ" "add" "member")
(("2" (iff)
(("2" (prop)
(("2" (typepred "T0")
(("2" (expand* "tower?" "member")
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(("2"
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(split)
(("1"
(inst - "chain_union(T0)")
(("1"
(expand "chain_union" 1)
(("1"
(expand* "extend" "Union")
(("1"
(inst
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"succ(chain_union(T0))")
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(expand*
"succ"
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(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
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nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T0 const-decl "(tower?)" zorn nil)
(tower? const-decl "bool" zorn nil)
(chain_union const-decl "subchain" chain_chain nil)
(chain_chain nonempty-type-eq-decl nil chain_chain nil)
(chain_incl const-decl "bool" chain_chain nil)
(subchain nonempty-type-eq-decl nil chain_chain nil)
(chain? const-decl "bool" chain nil)
(<= formal-const-decl "(partial_order?[T])" zorn nil)
(partial_order? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types 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-type-decl nil zorn nil)
(maximal_chain_add_set formula-decl nil zorn nil)
(T0_chain name-judgement "chain_chain" zorn nil)
(empty_succ formula-decl nil zorn nil)
(succ const-decl "subchain" zorn nil)
(FALSE const-decl "bool" booleans nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(extend const-decl "R" extend nil)
(Union const-decl "set" sets nil)
(finite_emptyset name-judgement "finite_set" finite_sets nil)
(finite_emptyset name-judgement "finite_set[T]" zorn nil)
(bounded_chain_upto formula-decl nil zorn nil)
(maximal_upto_subset formula-decl nil zorn nil)
(TRUE const-decl "bool" booleans nil)
(subset? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(upto const-decl "(LAMBDA (S): prefix?(S, ord))" ordered_subset
nil)
(union const-decl "set" sets nil)
(reflexive_closure const-decl "(reflexive?)" closure_ops nil)
(preorder? const-decl "bool" orders nil)
(transitive? const-decl "bool" relations nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
zorn nil)
(total_order? const-decl "bool" orders nil)
(dichotomous? const-decl "bool" orders nil)
(restrict const-decl "R" restrict nil)
(partial_order_restrict application-judgement "(partial_order?[S])"
restrict_order_props nil)
(preorder_restrict application-judgement "(preorder?[S])"
restrict_order_props nil)
(transitive_restrict application-judgement "(transitive?[S])"
restrict_order_props nil)
(antisymmetric_restrict application-judgement "(antisymmetric?[S])"
restrict_order_props nil)
(reflexive_restrict application-judgement "(reflexive?[S])"
restrict_order_props nil)
(reflexive? const-decl "bool" relations nil)
(antisymmetric? const-decl "bool" relations nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(r!1 skolem-const-decl "T" zorn nil)
(add const-decl "(nonempty?)" sets nil)
(nonempty? const-decl "bool" sets nil)
(fullset const-decl "set" sets nil)
(maximal? const-decl "bool" minmax_orders nil))
shostak)))
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