|
(digraph_ops
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("" (skosimp*)
(("" (expand "union")
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("2" (typepred "G2!1")
(("2" (inst?)
(("2" (assert)
(("2" (flatten) (("2" (assert) nil))))))))))))))))
nil)
((union const-decl "set" sets 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 digraph_ops nil)
(edgetype type-eq-decl nil digraphs nil)
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(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil)
(member const-decl "bool" sets nil))
nil))
(del_vert_TCC1 0
(del_vert_TCC1-1 nil 3253634004
("" (skosimp*)
(("" (lemma "finite_subset[edgetype[T]]")
(("" (inst?)
(("" (inst - "edges(G!1)")
(("" (assert) (("" (hide 2) (("" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((edgetype type-eq-decl nil digraphs nil)
(T formal-type-decl nil digraph_ops nil)
(finite_subset formula-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(subset? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(in? const-decl "bool" pairs nil) (pair type-eq-decl nil pairs nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil)
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(predigraph type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
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(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(del_vert_TCC2 0
(del_vert_TCC2-1 nil 3307703836 ("" (subtype-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
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(edgetype type-eq-decl nil digraphs nil)
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(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil)
(T formal-type-decl nil digraph_ops nil)
(in? const-decl "bool" pairs nil)
(/= const-decl "boolean" notequal nil)
(member const-decl "bool" sets nil)
(remove const-decl "set" sets nil))
nil))
(del_edge_TCC1 0
(del_edge_TCC1-1 nil 3253634004
("" (skosimp*)
(("" (expand "remove")
(("" (flatten)
(("" (expand "member")
(("" (typepred "G!1")
(("" (inst?) (("" (assert) nil))))))))))))
nil)
((remove const-decl "set" sets nil)
(member const-decl "bool" sets 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 digraph_ops nil)
(edgetype type-eq-decl nil digraphs nil)
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(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil))
nil))
(del_vert_still_in 0
(del_vert_still_in-1 nil 3253634004
("" (skosimp*)
(("" (expand "del_vert")
(("" (expand "remove")
(("" (expand "member") (("" (assert) nil))))))))
nil)
((del_vert const-decl "digraph[T]" digraph_ops nil)
(member const-decl "bool" sets nil)
(remove const-decl "set" sets nil))
nil))
(size_del_vert 0
(size_del_vert-1 nil 3253634004
("" (skosimp*)
(("" (typepred "v!1")
(("" (expand "del_vert")
(("" (expand "size") (("" (rewrite "card_remove") nil))))))))
nil)
((digraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(predigraph type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(edgetype type-eq-decl nil digraphs nil)
(T formal-type-decl nil digraph_ops nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(size const-decl "nat" digraphs nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(card_remove formula-decl nil finite_sets nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(del_vert const-decl "digraph[T]" digraph_ops nil))
nil))
(del_vert_le 0
(del_vert_le-1 nil 3253634004
("" (skosimp*)
(("" (expand "size")
(("" (expand "del_vert")
(("" (rewrite "card_remove")
(("" (lift-if) (("" (ground) nil))))))))))
nil)
((size const-decl "nat" digraphs nil)
(card_remove formula-decl nil finite_sets nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(edgetype type-eq-decl nil digraphs nil)
(predigraph type-eq-decl nil digraphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil)
(T formal-type-decl nil digraph_ops nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(del_vert const-decl "digraph[T]" digraph_ops nil))
nil))
(del_vert_ge 0
(del_vert_ge-1 nil 3253634004
("" (skosimp*)
(("" (expand "size")
(("" (expand "del_vert")
(("" (rewrite "card_remove")
(("" (lift-if) (("" (ground) nil))))))))))
nil)
((size const-decl "nat" digraphs nil)
(card_remove formula-decl nil finite_sets nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(edgetype type-eq-decl nil digraphs nil)
(predigraph type-eq-decl nil digraphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil)
(T formal-type-decl nil digraph_ops nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(del_vert const-decl "digraph[T]" digraph_ops nil))
nil))
(edge_in_del_vert 0
(edge_in_del_vert-1 nil 3253634004
("" (skosimp*) (("" (expand "del_vert") (("" (assert) nil)))) nil)
((del_vert const-decl "digraph[T]" digraph_ops nil)) nil))
(edges_del_vert 0
(edges_del_vert-1 nil 3253634004
("" (skosimp*)
(("" (expand "del_vert") (("" (flatten) (("" (propax) nil))))))
nil)
((del_vert const-decl "digraph[T]" digraph_ops nil)) nil))
(del_vert_comm 0
(del_vert_comm-1 nil 3253634004
("" (skosimp*)
(("" (apply-extensionality 1 :hide? t)
(("1" (expand "del_vert")
(("1" (apply-extensionality 1 :hide? t)
(("1" (iff 1) (("1" (ground) nil)))))))
("2" (expand "del_vert")
(("2" (apply-extensionality 1 :hide? t)
(("2" (grind) nil))))))))
nil)
((T formal-type-decl nil digraph_ops nil)
(edgetype type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(del_vert const-decl "digraph[T]" digraph_ops nil)
(digraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(in? const-decl "bool" pairs nil) (pair type-eq-decl nil pairs nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(remove const-decl "set" sets nil) (set type-eq-decl nil sets nil)
(finite_remove application-judgement "finite_set" finite_sets nil)
(/= const-decl "boolean" notequal nil)
(member const-decl "bool" sets nil))
nil))
(del_vert_empty? 0
(del_vert_empty?-1 nil 3253634004
("" (skosimp*)
(("" (lemma "card_empty?[T]")
(("" (inst?)
(("" (replace -1 * rl)
(("" (hide -1)
(("" (expand "singleton?")
(("" (expand "size")
(("" (lemma "size_del_vert")
(("" (inst?)
(("" (expand "size")
(("" (assert) nil))))))))))))))))))))
nil)
((T formal-type-decl nil digraph_ops nil)
(card_empty? formula-decl nil finite_sets nil)
(singleton? const-decl "bool" digraphs nil)
(size_del_vert formula-decl nil digraph_ops nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(size const-decl "nat" digraphs nil)
(del_vert const-decl "digraph[T]" digraph_ops nil)
(digraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(predigraph type-eq-decl nil digraphs nil)
(edgetype type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(del_edge_lem 0
(del_edge_lem-1 nil 3253634004
("" (skosimp*)
(("" (expand "member")
(("" (expand "del_edge")
(("" (expand "remove") (("" (propax) nil))))))))
nil)
((member const-decl "bool" sets nil)
(remove const-decl "set" sets nil)
(del_edge const-decl "digraph[T]" digraph_ops nil))
nil))
(del_edge_lem2 0
(del_edge_lem2-1 nil 3253634004
("" (skosimp*) (("" (grind) nil)) nil)
((finite_remove application-judgement "finite_set" finite_sets nil)
(remove const-decl "set" sets nil)
(member const-decl "bool" sets nil)
(/= const-decl "boolean" notequal nil)
(del_edge const-decl "digraph[T]" digraph_ops nil))
nil))
(del_edge_lem3 0
(del_edge_lem3-1 nil 3253634004
("" (skosimp*) (("" (grind) nil)) nil)
((finite_remove application-judgement "finite_set" finite_sets nil)
(remove const-decl "set" sets nil)
(member const-decl "bool" sets nil)
(del_edge const-decl "digraph[T]" digraph_ops nil))
nil))
(del_edge_lem5 0
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("" (skosimp*)
(("" (apply-extensionality 2 :hide? t)
(("1" (apply-extensionality 1 :hide? t)
(("1" (expand "del_edge") (("1" (grind) nil)))))
("2" (expand "del_edge") (("2" (propax) nil))))))
nil)
((T formal-type-decl nil digraph_ops nil)
(edgetype type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(del_edge const-decl "digraph[T]" digraph_ops nil)
(digraph type-eq-decl nil digraphs nil)
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(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(finite_remove application-judgement "finite_set" finite_sets nil)
(/= const-decl "boolean" notequal nil)
(member const-decl "bool" sets nil)
(remove const-decl "set" sets nil) (set type-eq-decl nil sets nil))
nil))
(vert_del_edge 0
(vert_del_edge-1 nil 3253634004 ("" (grind) nil nil)
((del_edge const-decl "digraph[T]" digraph_ops nil)) nil))
(del_edge_num 0
(del_edge_num-1 nil 3253634004
("" (skosimp*)
(("" (expand "num_edges")
((""
(case-replace
"edges(del_edge(G!1,e!1)) = remove(e!1,edges(G!1))")
(("1" (rewrite "card_remove[edgetype[T]]") nil)
("2" (hide 2)
(("2" (apply-extensionality :hide? t)
(("2" (iff 1)
(("2" (prop)
(("1" (lemma "del_edge_lem2")
(("1" (inst?)
(("1" (lemma "del_edge_lem")
(("1" (inst?)
(("1" (expand "member")
(("1" (assert)
(("1" (grind :exclude ("edges" "del_edge"))
nil)))))))))))))
("2" (rewrite "del_edge_lem3")
(("1" (hide 2) (("1" (grind :exclude "edges") nil)))
("2" (hide 2)
(("2" (grind :exclude "edges")
nil))))))))))))))))))
nil)
((num_edges const-decl "nat" digraph_ops nil)
(del_edge_lem3 formula-decl nil digraph_ops nil)
(/= const-decl "boolean" notequal nil)
(del_edge_lem2 formula-decl nil digraph_ops nil)
(del_edge_lem formula-decl nil digraph_ops nil)
(member const-decl "bool" sets nil)
(is_finite const-decl "bool" finite_sets nil)
(card_remove formula-decl nil finite_sets nil)
(remove const-decl "set" sets nil)
(del_edge const-decl "digraph[T]" digraph_ops nil)
(digraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(predigraph type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(edgetype type-eq-decl nil digraphs nil)
(T formal-type-decl nil digraph_ops nil)
(finite_remove application-judgement "finite_set" finite_sets nil))
nil))
(del_edge_singleton 0
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(("" (expand "singleton?")
(("" (expand "size")
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nil)
((singleton? const-decl "bool" digraphs nil)
(del_edge const-decl "digraph[T]" digraph_ops nil)
(size const-decl "nat" digraphs nil))
nil))
(del_vert_edge_comm 0
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(("" (apply-extensionality 1 :hide? t)
(("1" (apply-extensionality :hide? t) (("1" (grind) nil)))
("2" (expand "del_edge")
(("2" (expand "del_vert") (("2" (propax) nil))))))))
nil)
((T formal-type-decl nil digraph_ops nil)
(edgetype type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(del_edge const-decl "digraph[T]" digraph_ops nil)
(del_vert const-decl "digraph[T]" digraph_ops nil)
(digraph type-eq-decl nil digraphs nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(finite_remove application-judgement "finite_set" finite_sets nil)
(/= const-decl "boolean" notequal nil)
(member const-decl "bool" sets nil)
(remove const-decl "set" sets nil)
(in? const-decl "bool" pairs nil) (set type-eq-decl nil sets nil))
nil))
(del_vert_edge 0
(del_vert_edge-1 nil 3253634004
("" (skosimp*)
(("" (rewrite "del_vert_edge_comm")
(("" (apply-extensionality 1 :hide? t)
(("1" (apply-extensionality 1 :hide? t) (("1" (grind) nil)))
("2" (expand "del_edge") (("2" (propax) nil))))))))
nil)
((del_vert_edge_comm formula-decl nil digraph_ops nil)
(T formal-type-decl nil digraph_ops nil)
(edgetype type-eq-decl nil digraphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(predigraph type-eq-decl nil digraphs nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(digraph type-eq-decl nil digraphs nil)
(set type-eq-decl nil sets nil)
(finite_remove application-judgement "finite_set" finite_sets nil)
(in? const-decl "bool" pairs nil)
(/= const-decl "boolean" notequal nil)
(member const-decl "bool" sets nil)
(remove const-decl "set" sets nil)
(del_edge const-decl "digraph[T]" digraph_ops nil)
(del_vert const-decl "digraph[T]" digraph_ops nil))
nil)))
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