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(graph_conn_piece
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(singleton_piece-1 nil 3251050559
("" (skosimp*)
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(("1"
(hide -5)
(("1" (grind) nil)))
("2" (assert) nil)))
("2"
(assert)
nil))))))))))))))))))))))))))))))))))))))))
nil)
((finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(piece_connected? const-decl "bool" graph_conn_defs nil)
(empty? const-decl "bool" sets nil)
(empty? const-decl "bool" graphs nil)
(member const-decl "bool" sets nil)
(intersection const-decl "set" sets nil)
(card_one formula-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(union const-decl "graph[T]" graph_ops nil)
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(singleton const-decl "(singleton?)" sets nil)
(union const-decl "set" sets nil)
(nonempty_singleton_finite application-judgement
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(finite_union application-judgement "finite_set" finite_sets nil)
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(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(dbl const-decl "set[T]" doubletons nil)
(doubleton type-eq-decl nil doubletons nil)
(finite_set type-eq-decl nil finite_sets nil)
(pregraph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(graph type-eq-decl nil graphs nil)
(T formal-type-decl nil graph_conn_piece nil)
(size const-decl "nat" graphs nil)
(singleton? const-decl "bool" graphs nil))
nil))
(not_piece_has_2 0
(not_piece_has_2-2 nil 3251107139
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(hide 2)
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(("2"
(expand "empty?")
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nil))
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nil))
nil))
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nil))
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nil))
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nil))
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((finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(piece_connected? const-decl "bool" graph_conn_defs nil)
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(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
(Card const-decl "nat" finite_sets nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(is_finite const-decl "bool" finite_sets nil)
(>= const-decl "bool" reals 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)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(union const-decl "graph[T]" graph_ops nil)
(intersection const-decl "set" sets nil)
(card_empty? formula-decl nil finite_sets nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(card_union formula-decl nil finite_sets nil)
(size const-decl "nat" graphs nil)
(T formal-type-decl nil graph_conn_piece nil)
(graph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(doubleton type-eq-decl nil doubletons nil)
(dbl const-decl "set[T]" doubletons nil)
(= const-decl "[T, T -> boolean]" equalities nil)
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(AND const-decl "[bool, bool -> bool]" booleans nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
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(empty?_rew formula-decl nil graphs nil))
nil)
(not_piece_has_2-1 nil 3251050559
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(("2"
(expand "empty?")
(("2" (propax) nil nil))
nil))
nil))
nil)
("3"
(rewrite "finite_intersection")
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((piece_connected? const-decl "bool" graph_conn_defs nil)
(union const-decl "graph[T]" graph_ops nil)
(size const-decl "nat" graphs nil)
(graph type-eq-decl nil graphs nil)
(pregraph type-eq-decl nil graphs nil)
(doubleton type-eq-decl nil doubletons nil)
(dbl const-decl "set[T]" doubletons nil)
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(edge_not_across 0
(edge_not_across-1 nil 3251050559
("" (skosimp*)
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(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
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(lem1 0
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(("2" (apply-extensionality 1 :hide? t)
(("2" (grind) nil)))))))))
("2" (hide 1 2 3) (("2" (grind) nil))))))
nil)
((graph type-eq-decl nil graphs nil)
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(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(doubleton type-eq-decl nil doubletons nil)
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(union const-decl "graph[T]" graph_ops nil)
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(finite_remove application-judgement "finite_set" finite_sets nil)
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(union const-decl "set" sets nil)
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(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(intersection const-decl "set" sets nil)
(empty? const-decl "bool" sets nil))
nil))
(H1P_not_empty 0
(H1P_not_empty-1 nil 3251050559
("" (skosimp*)
(("" (hide -3 3)
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(expand "empty?")
(("1"
(expand "empty?")
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(grind)
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("2"
(hide -4 3 4)
(("2"
(expand "empty?")
(("2"
(expand "empty?")
(("2"
(inst -4 "x!1")
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(expand "member")
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(grind)
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("2" (hide -4 -6 2 3)
(("2" (lemma "edge_not_across")
(("2" (inst?)
(("2" (inst?)
(("2" (assert) nil))))))))))))))))))))))
nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
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(AND const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(dbl const-decl "set[T]" doubletons nil)
(doubleton type-eq-decl nil doubletons nil)
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(pregraph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(graph type-eq-decl nil graphs nil)
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(edge_not_across formula-decl nil graph_conn_piece nil)
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(empty? const-decl "bool" sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(deg_edge_exists formula-decl nil graph_deg nil)
(T formal-type-decl nil graph_conn_piece nil))
nil))
(cip0 0
(cip0-1 nil 3251050559
("" (skosimp*)
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(("1"
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("2" (hide -5 -6 -7 -8)
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(expand "empty?")
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(("1"
(inst?)
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(grind)
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("2" (reveal -3 -4)
(("2" (lemma "H1P_not_empty")
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(("2"
(inst -1 "G!1" "H2!1")
(("2"
(assert)
nil)))))))))))))))))))))))
("2" (hide -5 -6 -8)
(("2" (lemma "lem1")
(("2" (inst -1 "H1!1" "H2!1" "vo!1")
(("2" (assert) nil))))))))))))))
nil)
((del_vert const-decl "graph[T]" graph_ops nil)
(graph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(doubleton type-eq-decl nil doubletons nil)
(dbl const-decl "set[T]" doubletons nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(/= const-decl "boolean" notequal nil)
(AND const-decl "[bool, bool -> bool]" booleans 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 graph_conn_piece nil)
(union const-decl "graph[T]" graph_ops nil)
(H1P_not_empty formula-decl nil graph_conn_piece nil)
(finite_remove application-judgement "finite_set" finite_sets nil)
(remove const-decl "set" sets nil)
(intersection const-decl "set" sets nil)
(empty? const-decl "bool" sets nil)
(finite_union application-judgement "finite_set" finite_sets nil)
(union const-decl "set" sets nil)
(member const-decl "bool" sets nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(card_remove formula-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(size const-decl "nat" graphs nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(piece_connected? const-decl "bool" graph_conn_defs nil)
(lem1 formula-decl nil graph_conn_piece nil))
nil))
(cip3 0
(cip3-1 nil 3251050559
("" (skosimp*)
(("" (case "vert(H1!1)(vo!1)")
(("1" (lemma "cip0")
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("2" (lemma "cip0")
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(("2" (rewrite "intersection_commutative")
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(case-replace "union(H2!1, H1!1) = union(H1!1, H2!1)")
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(("1" (hide -1 -2 -3 -4 -7)
(("1" (replace -1)
(("1" (hide -1) (("1" (grind) nil)))))))))))
("2" (hide -1 -2 -3 -4 -5 -6 -7 -8 -9 2 3 4)
(("2" (expand "union")
(("2" (prop)
(("1" (rewrite "union_commutative") nil)
("2" (rewrite "union_commutative")
nil))))))))))))))))))
nil)
((graph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(doubleton type-eq-decl nil doubletons nil)
(dbl const-decl "set[T]" doubletons nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(/= const-decl "boolean" notequal nil)
(AND const-decl "[bool, bool -> bool]" booleans 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 graph_conn_piece nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(cip0 formula-decl nil graph_conn_piece nil)
(union const-decl "graph[T]" graph_ops nil)
(member const-decl "bool" sets nil)
(empty? const-decl "bool" sets nil)
(empty? const-decl "bool" graphs nil)
(union const-decl "set" sets nil)
(finite_union application-judgement "finite_set" finite_sets nil)
(union_commutative formula-decl nil sets_lemmas nil)
(intersection_commutative formula-decl nil sets_lemmas nil))
nil))
(connected_not_empty 0
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nil)
((empty? const-decl "bool" graphs nil)
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(card_empty? formula-decl nil finite_sets nil)
(size const-decl "nat" graphs nil)
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(graph type-eq-decl nil graphs nil)
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(doubleton type-eq-decl nil doubletons nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
(/= const-decl "boolean" notequal nil)
(AND const-decl "[bool, bool -> bool]" booleans 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)
(connected? def-decl "bool" graph_conn_defs nil))
nil))
(conn_implies_piece 0
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("" (induct "G" 1 "graph_induction_vert")
(("" (skosimp*)
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("2"
(lemma "cip3")
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(inst
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(("2"
(case-replace
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(("1"
(apply-extensionality
1
:hide?
t)
(("1"
(grind)
nil)))))
("2"
(hide
-1
-2
-3
-4
-5
-6
-7
-8
2
3
4)
(("2"
(apply-extensionality
1
:hide?
t)
(("2"
(grind)
nil)))))))))))))
("2"
(hide
-1
-2
-3
-4
-5
-6
-7
-8
1
3
4
5)
(("2"
(apply-extensionality
1
:hide?
t)
(("2"
(grind)
nil)))))))))
("2"
(hide
-1
-2
-3
-4
-5
-6
-7
-8
2
3
4)
(("2"
(apply-extensionality
1
:hide?
t)
(("1"
(apply-extensionality
1
:hide?
t)
(("1" (grind) nil)))
("2"
(apply-extensionality
1
:hide?
t)
(("2"
(grind)
nil))))))))))))))))))))))))))))))))))))))))))
nil)
((not_piece_has_2 formula-decl nil graph_conn_piece nil)
(connected_not_empty formula-decl nil graph_conn_piece nil)
(union const-decl "graph[T]" graph_ops nil)
(empty? const-decl "bool" graphs nil)
(empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(intersection const-decl "set" sets nil)
(union const-decl "set" sets nil)
(finite_union application-judgement "finite_set" finite_sets nil)
(cip3 formula-decl nil graph_conn_piece nil)
(singleton_piece formula-decl nil graph_conn_piece nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(> const-decl "bool" reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(deg const-decl "nat" graph_deg nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(del_vert const-decl "graph[T]" graph_ops nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(graph_induction_vert formula-decl nil graph_inductions nil)
(T formal-type-decl nil graph_conn_piece nil)
(piece_connected? const-decl "bool" graph_conn_defs nil)
(connected? def-decl "bool" graph_conn_defs nil)
(pred type-eq-decl nil defined_types nil)
(graph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(doubleton type-eq-decl nil doubletons nil)
(dbl const-decl "set[T]" doubletons nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(/= const-decl "boolean" notequal nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil)))
¤ Dauer der Verarbeitung: 0.40 Sekunden
(vorverarbeitet)
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