(relations_extra
(strict_order_is_asymmetric 0
(strict_order_is_asymmetric-1 nil 3308139199
("" (skosimp* t)
(("" (expand "strict_order?" )
(("" (flatten)
(("" (expand "asymmetric?" )
(("" (skosimp*)
(("" (expand "transitive?" )
(("" (inst - "x!2" "y!1" "x!2" )
(("" (assert )
(("" (expand "irreflexive?" ) (("" (inst?) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((asymmetric? const-decl "bool" relations_extra nil )
(transitive? const-decl "bool" relations nil )
(irreflexive? const-decl "bool" relations 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(strict_order? const-decl "bool" orders nil ))
shostak))
(asymmetric_is_antisymmetric 0
(asymmetric_is_antisymmetric-1 nil 3308139286
("" (skosimp* t)
(("" (expand "asymmetric?" )
(("" (expand "antisymmetric?" )
(("" (skosimp*) (("" (inst?) (("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
((antisymmetric? const-decl "bool" relations 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(asymmetric? const-decl "bool" relations_extra nil ))
shostak))
(asymmetric_is_irreflexive 0
(asymmetric_is_irreflexive-1 nil 3308139358
("" (skosimp* t)
(("" (expand "irreflexive?" )
(("" (expand "asymmetric?" )
(("" (skosimp*) (("" (inst?) (("" (prop) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((irreflexive? const-decl "bool" relations 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(asymmetric? const-decl "bool" relations_extra nil ))
shostak))
(reflexive 0
(reflexive-3 nil 3308138472
("" (skolem-typepred)
(("" (expand "reflexive?" ) (("" (propax) nil nil )) nil )) nil )
((reflexive? const-decl "bool" relations nil )
(PRED type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(reflexive-2 nil 3308137563
("" (skosimp* t)
(("" (auto-rewrite-defs) (("" (assert ) (("" (inst?) nil nil )) nil ))
nil ))
nil )
nil nil )
(reflexive-1 nil 3308137369 ("" (grind) nil nil ) nil shostak))
(irreflexive 0
(irreflexive-3 nil 3308138470
("" (skolem-typepred)
(("" (expand "irreflexive?" ) (("" (propax) nil nil )) nil )) nil )
((irreflexive? const-decl "bool" relations nil )
(PRED type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(irreflexive-2 nil 3308137556
("" (skosimp* t)
(("" (auto-rewrite-defs) (("" (assert ) (("" (inst?) nil nil )) nil ))
nil ))
nil )
nil nil )
(irreflexive-1 nil 3308137450 ("" (grind) nil nil ) nil nil ))
(symmetric 0
(symmetric-2 nil 3308138467
("" (skolem-typepred)
(("" (expand "symmetric?" ) (("" (propax) nil nil )) nil )) nil )
((symmetric? const-decl "bool" relations nil )
(PRED type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(symmetric-1 nil 3308137453
("" (skosimp* t)
(("" (auto-rewrite-defs)
(("" (assert )
(("" (inst - "x!1" "y!1" ) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil )
nil nil ))
(antisymmetric 0
(antisymmetric-2 nil 3308138464
("" (skolem-typepred)
(("" (expand "antisymmetric?" ) (("" (propax) nil nil )) nil )) nil )
((antisymmetric? const-decl "bool" relations nil )
(PRED type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(antisymmetric-1 nil 3308137572
("" (skosimp* t)
(("" (auto-rewrite-defs)
(("" (assert ) (("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil )
nil nil ))
(asymmetric 0
(asymmetric-1 nil 3308139089
("" (skolem-typepred)
(("" (expand "asymmetric?" ) (("" (propax) nil nil )) nil )) nil )
((asymmetric? const-decl "bool" relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
shostak))
(transitive 0
(transitive-2 nil 3308138460
("" (skolem-typepred)
(("" (expand "transitive?" ) (("" (propax) nil nil )) nil )) nil )
((transitive? const-decl "bool" relations nil )
(PRED type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(transitive-1 nil 3308137577
("" (skosimp* t)
(("" (auto-rewrite-defs)
(("" (assert )
(("" (inst - "x!1" "y!1" "z!1" ) (("" (assert ) nil nil )) nil ))
nil ))
nil ))
nil )
nil nil ))
(dichotomous 0
(dichotomous-2 nil 3308138452
("" (skolem-typepred)
(("" (expand "dichotomous?" ) (("" (propax) nil nil )) nil )) nil )
((dichotomous? const-decl "bool" orders nil )
(pred type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(dichotomous-1 nil 3308137580
("" (skosimp* t)
(("" (auto-rewrite-defs)
(("" (assert ) (("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil )
nil nil ))
(trichotomous 0
(trichotomous-2 nil 3308138441
("" (skolem-typepred)
(("" (expand "trichotomous?" ) (("" (propax) nil nil )) nil )) nil )
((trichotomous? const-decl "bool" orders nil )
(pred type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
nil )
(trichotomous-1 nil 3308137584
("" (skosimp* t)
(("" (auto-rewrite-defs)
(("" (assert ) (("" (inst?) (("" (assert ) nil nil )) nil )) nil ))
nil ))
nil )
nil nil ))
(dichotomous_is_trichotomous 0
(dichotomous_is_trichotomous-1 nil 3308166081
("" (skosimp* t)
(("" (expand * "trichotomous?" "dichotomous?" )
(("" (skosimp*) (("" (inst?) (("" (prop) nil nil )) nil )) nil ))
nil ))
nil )
((trichotomous? const-decl "bool" orders 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(dichotomous? const-decl "bool" orders nil ))
shostak))
(well_founded 0
(well_founded-1 nil 3308138322
("" (skolem-typepred)
(("" (expand "well_founded?" ) (("" (propax) nil nil )) nil )) nil )
((well_founded? const-decl "bool" orders nil )
(pred type-eq-decl nil defined_types nil )
(T formal-type-decl nil relations_extra nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil ))
shostak))
(reflexive_closure_TCC1 0
(reflexive_closure_TCC1-1 nil 3308173829 ("" (subtype-tcc) nil nil )
((member const-decl "bool" sets nil )
(union const-decl "set" sets nil )
(reflexive? const-decl "bool" relations nil ))
shostak))
(irreflexive_kernel_TCC1 0
(irreflexive_kernel_TCC1-1 nil 3308173829 ("" (subtype-tcc) nil nil )
((member const-decl "bool" sets nil )
(difference const-decl "set" sets nil )
(irreflexive? const-decl "bool" relations nil ))
shostak))
(symmetric_closure_TCC1 0
(symmetric_closure_TCC1-1 nil 3308173829 ("" (subtype-tcc) nil nil )
((member const-decl "bool" sets nil )
(converse const-decl "pred[[T2, T1]]" relation_defs nil )
(union const-decl "set" sets nil )
(symmetric? const-decl "bool" relations nil ))
shostak))
(symmetric_kernel_TCC1 0
(symmetric_kernel_TCC1-1 nil 3308173829 ("" (subtype-tcc) nil nil )
((member const-decl "bool" sets nil )
(converse const-decl "pred[[T2, T1]]" relation_defs nil )
(intersection const-decl "set" sets nil )
(symmetric? const-decl "bool" relations nil ))
shostak))
(reflexive_closure_preserves_transitive 0
(reflexive_closure_preserves_transitive-1 nil 3308174613
("" (skosimp* t)
((""
(expand * "preorder?" "transitive?" "reflexive_closure" "union"
"member" )
(("" (skosimp*)
(("" (inst - "x!1" "y!1" "z!1" )
(("" (assert ) (("" (ground) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((union const-decl "set" sets nil )
(member const-decl "bool" sets nil )
(reflexive_closure const-decl "(reflexive?)" relations_extra nil )
(preorder? const-decl "bool" orders 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 relations_extra nil )
(PRED type-eq-decl nil defined_types nil )
(transitive? const-decl "bool" relations nil ))
shostak))
(strict_order_to_partial_order 0
(strict_order_to_partial_order-1 nil 3308174139
("" (skosimp* t)
(("" (expand * "partial_order?" "preorder?" )
((""
(expand * "antisymmetric?" "reflexive_closure" "union" "member" )
(("" (skosimp*)
(("" (assert )
(("" (use "asymmetric" ) (("" (prop) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil )
((reflexive_closure_preserves_transitive application-judgement
"(preorder?)" relations_extra nil )
(partial_order? const-decl "bool" orders nil )
(asymmetric formula-decl nil relations_extra nil )
(asymmetric? const-decl "bool" relations_extra nil )
(antisymmetric? const-decl "bool" relations nil )
(union const-decl "set" sets nil )
(member const-decl "bool" sets nil )
(reflexive_closure const-decl "(reflexive?)" relations_extra 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(strict_order? const-decl "bool" orders nil ))
shostak))
(reflexive_closure_dichotomous 0
(reflexive_closure_dichotomous-1 nil 3308223765
("" (skosimp*)
(("" (expand * "dichotomous?" "reflexive_closure" "union" "member" )
(("" (skosimp*)
(("" (use "trichotomous" ) (("" (prop) nil nil )) nil )) nil ))
nil ))
nil )
((reflexive_closure const-decl "(reflexive?)" relations_extra nil )
(member const-decl "bool" sets nil )
(union const-decl "set" sets nil )
(dichotomous? const-decl "bool" orders nil )
(trichotomous formula-decl nil relations_extra nil )
(trichotomous? const-decl "bool" orders nil )
(pred type-eq-decl nil defined_types nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil relations_extra nil ))
nil ))
(strict_total_order_to_total_order 0
(strict_total_order_to_total_order-1 nil 3308223200
("" (skosimp*)
(("" (expand "total_order?" ) (("" (propax) nil nil )) nil )) nil )
((reflexive_closure_dichotomous application-judgement
"(dichotomous?)" relations_extra nil )
(strict_order_to_partial_order application-judgement
"(partial_order?)" relations_extra nil )
(total_order? const-decl "bool" orders nil ))
shostak))
(partial_order_to_strict_order 0
(partial_order_to_strict_order-1 nil 3308174139
("" (skosimp* t)
((""
(expand * "strict_order?" "transitive?" "irreflexive_kernel"
"difference" "member" )
(("" (skosimp*)
(("" (lemma "transitive" )
(("" (assert )
(("" (inst - "R!1" "x!1" "y!1" "z!1" )
(("" (assert )
(("" (replace -5 :hide? t)
(("" (lemma "antisymmetric" )
(("" (inst - "R!1" "z!1" "y!1" )
(("" (prop) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((transitive? const-decl "bool" relations nil )
(difference const-decl "set" sets nil )
(member const-decl "bool" sets nil )
(irreflexive_kernel const-decl "(irreflexive?)" relations_extra
nil )
(strict_order? const-decl "bool" orders nil )
(transitive formula-decl nil relations_extra nil )
(PRED type-eq-decl nil defined_types nil )
(antisymmetric? const-decl "bool" relations nil )
(antisymmetric formula-decl nil relations_extra 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(partial_order? const-decl "bool" orders nil ))
shostak))
(irreflexive_kernel_trichotomous 0
(irreflexive_kernel_trichotomous-1 nil 3308223871
("" (skosimp*)
((""
(expand * "trichotomous?" "irreflexive_kernel" "difference"
"member" )
(("" (skosimp*)
(("" (assert )
(("" (use "dichotomous" ) (("" (prop) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
((irreflexive_kernel const-decl "(irreflexive?)" relations_extra
nil )
(member const-decl "bool" sets nil )
(difference const-decl "set" sets nil )
(trichotomous? const-decl "bool" orders nil )
(T formal-type-decl nil relations_extra nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(pred type-eq-decl nil defined_types nil )
(dichotomous? const-decl "bool" orders nil )
(dichotomous formula-decl nil relations_extra nil ))
nil ))
(total_order_to_strict_total_order 0
(total_order_to_strict_total_order-1 nil 3308223398
("" (skosimp*)
(("" (expand "strict_total_order?" ) (("" (propax) nil nil )) nil ))
nil )
((irreflexive_kernel_trichotomous application-judgement
"(trichotomous?)" relations_extra nil )
(partial_order_to_strict_order application-judgement
"(strict_order?)" relations_extra nil )
(strict_total_order? const-decl "bool" orders nil ))
shostak))
(symmetric_kernel_of_preorder 0
(symmetric_kernel_of_preorder-1 nil 3308174139
("" (skosimp* t)
(("" (expand "equivalence?" )
(("" (prop)
(("1"
(expand * "reflexive?" "symmetric_kernel" "intersection"
"converse" "member" )
(("1" (skosimp*)
(("1" (use "reflexive" ) (("1" (prop) nil nil )) nil )) nil ))
nil )
("2"
(expand * "transitive?" "symmetric_kernel" "intersection"
"converse" "member" )
(("2" (skosimp*)
(("2" (lemma "transitive" )
(("2" (inst-cp - "R!1" "x!1" "y!1" "z!1" )
(("2" (inst - "R!1" "z!1" "y!1" "x!1" )
(("2" (prop) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((equivalence? const-decl "bool" relations nil )
(transitive? const-decl "bool" relations nil )
(transitive formula-decl nil relations_extra nil )
(symmetric_kernel const-decl "(symmetric?)" relations_extra nil )
(converse const-decl "pred[[T2, T1]]" relation_defs nil )
(member const-decl "bool" sets nil )
(intersection const-decl "set" sets nil )
(reflexive? const-decl "bool" relations nil )
(reflexive formula-decl nil relations_extra nil )
(PRED type-eq-decl nil defined_types 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 relations_extra nil )
(pred type-eq-decl nil defined_types nil )
(preorder? const-decl "bool" orders nil ))
shostak)))
quality 100%
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