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nil
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nil
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nil
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(("4"
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nil
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nil
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(expand
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((T formal-type-decl nil cycle_deg nil )
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(edge? const-decl "bool" graphs nil )
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(empty? const-decl "bool" graphs nil )
(below type-eq-decl nil naturalnumbers nil )
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(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 )
(Seq type-eq-decl nil walks nil )
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nil )
(number nonempty-type-decl nil numbers nil )
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(below type-eq-decl nil nat_types nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(real_gt_is_strict_total_order name-judgement
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(NOT const-decl "[bool -> bool]" booleans nil )
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(inst-cp
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"G!1"
"x!1"
"y!1"
"w!1" )
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(inst
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"G!1"
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(lemma "walk_merge" )
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(inst
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"G!1"
"w!4"
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"x!2"
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"x!1" )
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(("2"
(inst 1 "p!1" )
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(("1"
(assert )
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(bddsimp)
nil )))))
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(typepred
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(inst
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nil )))))
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(-1
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nil )))
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(assert
(-1
1))
nil )))))
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(assert )
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(hide
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(grind)
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(-1
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2)
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1)
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nil )
nil nil )
(reachable_conn-3 nil 3559570524
("" (skosimp*)
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(bddsimp)
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(lemma "walk?_reverse" )
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(inst-cp
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(inst
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"G!1"
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(inst
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nil )))))
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(bddsimp)
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(typepred
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(-1
-9
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-14
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(-1
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-)
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(assert )
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(reveal
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(inst
-1
"G!1"
"0"
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(inst
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(-1
-2
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-)
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2)
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(-5
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-15
-16
-17
-18))
(("2"
(assert )
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(bddsimp)
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(grind)
nil )
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(grind)
nil )))))))))
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(hide
2)
(("3"
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-2
-5
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-13
-14
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(("3"
(assert )
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(bddsimp)
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(typepred
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(reveal
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(propax)
nil )))))))))))))
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-4
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3)
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(hide
2)
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(assert )
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(bddsimp)
nil )))))))))
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(assert )
nil )
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(assert )
nil )
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(assert )
nil )
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(assert )
nil )))))
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(hide
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-9
-12
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2)
(("2"
(hide
-1)
(("2"
(grind)
nil )))))))))))))
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(-1
-2
1))
nil )))))
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(assert
(-1
1))
nil )))
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(assert
(-1
1))
nil )))))
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"n!1" )
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(assert )
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(bddsimp)
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(lemma
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(inst
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(typepred
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(inst
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nil )))
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(typepred
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(-1
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(expand
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1)
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(-14
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-)
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2)
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(grind)
nil )))))))))))))))))))))))))))
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(grind)
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(-1
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1)
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nil )
nil nil )
(reachable_conn-2 nil 3559570298
("" (skosimp*)
(("" (lemma "conn_eq_path" )
(("" (inst -1 "subgraph(G!1, reachable(G!1, x!1))" )
(("" (iff -1)
(("" (bddsimp)
(("" (hide 1)
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(("1" (bddsimp)
(("1"
(inst 1
"(#l := 1, seq :=(LAMBDA (i:below(1)): x!1)#)" )
(("1" (assert ) nil )))
("2" (typepred "x!1" )
(("2" (propax) nil )))))))))))
("2" (skosimp*)
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(("2"
(bddsimp)
(("2"
(skosimp*)
(("2"
(lemma "walk?_reverse" )
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(inst-cp
-1
"G!1"
"x!1"
"y!1"
"w!1" )
(("2"
(inst
-1
"G!1"
"x!1"
"x!2"
"w!2" )
(("2"
(bddsimp)
(("2"
(skosimp*)
(("2"
(lemma "walk_merge" )
(("2"
(inst
-1
"G!1"
"w!4"
"w!3"
"x!2"
"y!1"
"x!1" )
(("2"
(bddsimp)
(("2"
(skosimp*)
(("2"
(inst 1 "p!1" )
(("1"
(install-rewrites
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(("1"
(assert )
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(bddsimp)
nil )))))
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(assert )
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(install-rewrites
"walks" )
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(assert )
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(("1"
(bddsimp)
(("1"
(typepred
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(("1"
(inst
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"n!1" )
(("1"
(bddsimp)
nil )))))
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(skosimp*)
(("2"
(inst-cp
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"n!1" )
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(inst
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"1+n!1" )
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(("1"
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(("1"
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(("1"
(lemma
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(inst
-1
"G!1"
"0"
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(("1"
(inst
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(-4
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-12
-13
-14
-15
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-26)
-)
(("1"
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(("2"
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nil )))))))))
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-7
-8
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2)
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-9
-12
-13
-14
-15)
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(-1
-3)
-)
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(assert )
nil )))
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(reveal
-6
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(inst
-1
"G!1"
"0"
"1+n!1"
"p!1" )
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(inst
-3
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-2
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2)
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nil )
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nil )))))))))
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2)
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nil )))))))))))))
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-4
-12
-15
3)
(("4"
(reveal
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2)
(("4"
(assert )
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(bddsimp)
nil )))))))))
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(assert )
nil )))))
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-2
-9
-12
-15
2)
(("2"
(hide
-1)
(("2"
(grind)
nil )))))))))))))
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(assert
(-1
-2
1))
nil )))))
("2"
(assert
(-1
1))
nil )))
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(assert
(-1
1))
nil )))))
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-9
"n!1" )
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(assert )
nil )))))))
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nil )
nil nil )
(reachable_conn-1 nil 3312285132
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"G!1"
"x!1"
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(inst
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"G!1"
"w!4"
"w!3"
"x!2"
"y!1"
"x!1" )
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nil
nil ))
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nil )
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"n!1" )
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nil
nil ))
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nil
nil ))
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nil ))
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(("2"
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nil
nil ))
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nil )
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(-2
-7
-8
-19)
-)
(("2"
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2)
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nil ))
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(reveal
-10)
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(-16
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(hide-all-but
(-1
-9
-12
-13
-14
-15)
-)
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(hide
2)
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nil ))
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nil ))
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(-1
-3)
-)
(("2"
(assert )
nil
nil ))
nil )
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(reveal
-6
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(lemma
"walk?_caret" )
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(inst
-1
"G!1"
"0"
"1+n!1"
"p!1" )
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(inst
-3
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(-3
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-12
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"p!2" )
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nil
nil ))
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nil )
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(hide-all-but
-3
-)
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(grind)
nil
nil ))
nil ))
nil ))
nil ))
nil )
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(hide-all-but
(-1
-2
-5
-6
-7)
-)
(("2"
(hide
2)
(("2"
(assert )
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nil ))
nil ))
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nil )
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(hide
2)
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(hide
(-5
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-13
-14
-15
-16
-17
-18))
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2)
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-2
-5
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-13
-14
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nil )
("4"
(hide
-4
-12
-15
3)
(("4"
(reveal
-8)
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(hide
2)
(("4"
(assert )
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(bddsimp)
nil
nil ))
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(assert )
nil
nil )
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(assert )
nil
nil )
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nil )
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nil
nil ))
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-2
-9
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-15
2)
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-1)
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nil
nil ))
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(-1
-2
1))
nil
nil ))
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(assert
(-1
1))
nil
nil ))
nil )
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(assert
(-1
1))
nil
nil ))
nil ))
nil )
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(inst
-9
"n!1" )
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nil
nil ))
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"G!1"
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-4)
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-1
"G!1"
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1)
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(-1
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(expand
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1)
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(-14
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-16)
-)
(("2"
(hide
2)
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(grind)
nil
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nil ))
nil ))
nil ))
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nil )
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(grind)
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nil ))
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(reveal
-2)
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(hide-all-but
(-1
-10
-11
-12)
-)
(("2"
(hide
2)
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(grind)
nil
nil ))
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nil )
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2)
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"^"
1)
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nil ))
nil )
((conn_eq_path formula-decl nil graph_connected nil )
(edge? const-decl "bool" graphs nil )
(walk? const-decl "bool" walks nil )
(walk_from? const-decl "bool" walks nil )
(empty? const-decl "bool" graphs nil )
(Seq type-eq-decl nil walks nil )
(verts_in? const-decl "bool" walks nil )
(prewalk type-eq-decl nil walks nil )
(walk_merge formula-decl nil walks nil )
(nil application-judgement "finite_set[T]" graph_conn_piece nil )
(walk?_caret formula-decl nil walks nil )
(Walk type-eq-decl nil walks nil )
(walk?_reverse formula-decl nil walks nil )
(path_connected? const-decl "bool" graph_conn_defs nil )
(subgraph const-decl "Subgraph(G)" subgraphs nil )
(Subgraph type-eq-decl nil subgraphs nil )
(subgraph? const-decl "bool" subgraphs 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 ))
nil ))
(conn_compon 0
(conn_compon-3 nil 3312284893
("" (skosimp*)
(("" (inst 1 "subgraph(G!1,reachable(G!1,x!1))" )
(("" (bddsimp)
(("1" (skosimp*)
(("1" (typepred "y!1" )
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(("1"
(case "incident_edges(y!1, G!1) =
incident_edges(y!1, subgraph(G!1, reachable(G!1, x!1)))")
(("1"
(auto-rewrite-theories "finite_sets[doubleton[T]]" )
(("1" (replace -1 1) (("1" (propax) nil nil )) nil ))
nil )
("2" (hide 2)
(("2" (expand "incident_edges" )
(("2" (apply-extensionality 1 :hide? t)
(("2" (iff 1)
(("2" (bddsimp)
(("1" (expand "reachable" )
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(bddsimp)
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(case "y!1=x!3" )
(("1"
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(("1" (inst 1 "w!1" ) nil nil ))
nil )
("2"
(inst 2 "add1(w!1,x!3)" )
(("1"
(expand "walk_from?" )
(("1"
(assert )
(("1"
(bddsimp)
(("1"
(lemma "walk?_add1" )
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-1
"G!1"
"w!1"
"x!3" )
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(replace -7 1)
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-1
-6
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2)
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(("1"
(inst
-1
"x!2"
"x!3"
"y!1" )
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(bddsimp)
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"finite_sets[doubleton[T]].card_disj_union" )
(("2"
(inst
-1
"{e: doubleton[T] | edges(G!1)(e) AND e(v!1)}"
"{e: doubleton[T] | edges(G!1)(e) AND NOT e(v!1)}" )
(("1"
(bddsimp)
(("1"
(expand
"union"
-1)
(("1"
(expand
"member"
-1)
(("1"
(case
"{x: doubleton[T] |
edges(G!1)(x) AND x(v!1) OR edges(G!1)(x) AND NOT x(v!1)}=edges(G!1)")
(("1"
(replace
-1
-2)
(("1"
(hide
-1)
(("1"
(expand
"incident_edges"
-2)
(("1"
(replace
-2
-1)
(("1"
(assert
(-1
1))
nil )))))))))
("2"
(hide
-1
-2
-3
2)
(("2"
(grind)
(("2"
(apply-extensionality
1)
(("2"
(hide
2)
(("2"
(iff
1)
(("2"
(bddsimp)
nil )))))))))))))))))
("2"
(hide
-1
-2
2)
(("2"
(install-rewrites
"finite_sets[doubleton[T]]" )
(("2"
(assert )
(("2"
(skosimp*)
nil )))))))))
("2"
(lemma
"graph_deg[T].incident_edges_TCC1" )
(("2"
(inst
-1
--> --------------------
--> maximum size reached
--> --------------------
Messung V0.5 in Prozent C=100 H=100 G=100
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