:: GRAPH_4 semantic presentation
:: deftheorem Def1 defines orientedly_joins GRAPH_4:def 1 :
theorem Th1: :: GRAPH_4:1
:: deftheorem Def2 defines are_orientedly_incident GRAPH_4:def 2 :
theorem Th2: :: GRAPH_4:2
:: deftheorem Def3 defines -SVSet GRAPH_4:def 3 :
:: deftheorem Def4 defines -TVSet GRAPH_4:def 4 :
theorem Th3: :: GRAPH_4:3
canceled;
theorem Th4: :: GRAPH_4:4
:: deftheorem Def5 defines is_oriented_vertex_seq_of GRAPH_4:def 5 :
theorem Th5: :: GRAPH_4:5
theorem Th6: :: GRAPH_4:6
theorem Th7: :: GRAPH_4:7
theorem Th8: :: GRAPH_4:8
theorem Th9: :: GRAPH_4:9
theorem Th10: :: GRAPH_4:10
theorem Th11: :: GRAPH_4:11
:: deftheorem Def6 defines oriented-vertex-seq GRAPH_4:def 6 :
theorem Th12: :: GRAPH_4:12
theorem Th13: :: GRAPH_4:13
theorem Th14: :: GRAPH_4:14
theorem Th15: :: GRAPH_4:15
theorem Th16: :: GRAPH_4:16
Lemma109:
for G being Graph
for v being Element of the Vertices of G holds <*v*> is_oriented_vertex_seq_of {}
:: deftheorem Def7 defines Simple GRAPH_4:def 7 :
theorem Th17: :: GRAPH_4:17
canceled;
theorem Th18: :: GRAPH_4:18
theorem Th19: :: GRAPH_4:19
theorem Th20: :: GRAPH_4:20
theorem Th21: :: GRAPH_4:21
Lemma119:
for p being FinSequence
for m, n being Element of NAT st 1 <= m & m <= n + 1 & n <= len p holds
( (len (m,n -cut p)) + m = n + 1 & ( for i being Element of NAT st i < len (m,n -cut p) holds
(m,n -cut p) . (i + 1) = p . (m + i) ) )
theorem Th22: :: GRAPH_4:22
theorem Th23: :: GRAPH_4:23
theorem Th24: :: GRAPH_4:24
theorem Th25: :: GRAPH_4:25
theorem Th26: :: GRAPH_4:26