| | Some definitions of interest. |
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| equiv_rel | Def EquivRel x,y:T. E(x;y) == Refl(T;x,y.E(x;y)) & (Sym x,y:T. E(x;y)) & (Trans x,y:T. E(x;y)) |
| | | Thm*  T:Type, E:(T  TProp). (EquivRel x,y:T. E(x,y))  Prop |
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| graph | Def Graph == v:Type e:Type(evv)Top |
| | | Thm* Graph Type{i'} |
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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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| refl | Def Refl(T;x,y.E(x;y)) == a:T. E(a;a) |
| | | Thm* T:Type, E:(TTProp). Refl(T;x,y.E(x,y)) Prop |
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| sym | Def Sym x,y:T. E(x;y) == a,b:T. E(a;b)   E(b;a) |
| | | Thm* T:Type, E:(TTProp). (Sym x,y:T. E(x,y)) Prop |
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| trans | Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b) E(b;c) E(a;c) |
| | | Thm* T:Type, E:(TTProp). (Trans x,y:T. E(x,y)) Prop |
