| | Some definitions of interest. |
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| 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 |
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| 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 |
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| compose | Def (f o g)(x) == f(g(x)) |
| | | Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC |
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| compose2 | Def (f1,f2) o g(x) == g(x)/x,y. < f1(x),f2(y) > |
| | | Thm* A,B,C,B',C':Type, g:(AB C), f1:(BB'), f2:(CC'). (f1,f2) o g AB'C' |
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| rel-graph | Def Graph(x,y:T. R(x;y)) == < vertices = T, edges = {p:(TT)| R(1of(p);2of(p)) }, incidence = Id > |
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| tidentity | Def Id == Id |
| | | Thm* A:Type. Id AA |
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| identity | Def Id(x) == x |
| | | Thm* A:Type. Id AA |
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| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
