| | Who Cites graph-isomorphic? |
|
| graph-isomorphic | Def G  H ==  vmap:(Vertices(G)  Vertices(H)), emap:(Edges(G)Edges(H)). Bij(Vertices(G); Vertices(H); vmap) & Bij(Edges(G); Edges(H); emap) & (vmap,vmap) o Incidence(G) = Incidence(H) o emap |
|
| gr_f | Def Incidence(t) == 1of(2of(2of(t))) |
| | | Thm*  t:Graph. Incidence(t)  Edges(t)Vertices(t) Vertices(t) |
|
| compose | Def (f o g)(x) == f(g(x)) |
| | | Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC |
|
| compose2 | Def (f1,f2) o g(x) == g(x)/x,y. < f1(x),f2(y) > |
| | | Thm* A,B,C,B',C':Type, g:(ABC), f1:(BB'), f2:(CC'). (f1,f2) o g AB'C' |
|
| gr_v | Def Vertices(t) == 1of(t) |
| | | Thm* t:Graph. Vertices(t) Type |
|
| gr_e | Def Edges(t) == 1of(2of(t)) |
| | | Thm* t:Graph. Edges(t) Type |
|
| biject | Def Bij(A; B; f) == Inj(A; B; f) & Surj(A; B; f) |
| | | Thm* A,B:Type, f:(AB). Bij(A; B; f) Prop |
|
| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
|
| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
|
| surject | Def Surj(A; B; f) == b:B. a:A. f(a) = b |
| | | Thm* A,B:Type, f:(AB). Surj(A; B; f) Prop |
|
| inject | Def Inj(A; B; f) == a1,a2:A. f(a1) = f(a2) B   a1 = a2 |
| | | Thm* A,B:Type, f:(AB). Inj(A; B; f) Prop |
