Nuprl - Proof: graph-isomorphic inversion 1

(3steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

1. G: Graph
2. H: Graph
3. vmap: Vertices(G)Vertices(H)
4. emap: Edges(G)Edges(H)
5. Bij(Vertices(G); Vertices(H); vmap)
6. Bij(Edges(G); Edges(H); emap)
7. (vmap,vmap) o Incidence(G) = Incidence(H) o emap
8. g1: Edges(H)Edges(G)
9. Bij(Edges(H); Edges(G); g1)
10. InvFuns(Edges(G); Edges(H); emap; g1)
11. g: Vertices(H)Vertices(G)
12. Bij(Vertices(H); Vertices(G); g)
13. InvFuns(Vertices(G); Vertices(H); vmap; g)

(g,g) o Incidence(H) = Incidence(G) o g1

By: All (Unfold `inv_funs`)

Generated subgoal:

1 10. g1 o emap = Id
11. emap o g1 = Id
12. g: Vertices(H)Vertices(G)
13. Bij(Vertices(H); Vertices(G); g)
14. g o vmap = Id
15. vmap o g = Id
(g,g) o Incidence(H) = Incidence(G) o g1 1 step

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(3steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc