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At: fin alph list quo 1 1 1 1 1 3 1 1 1 1 1 1 1 1
1. Alph: Type
2. E: Alph*Alph*Prop
3. n:
4. f: nAlph
5. g: Alphn
6. g o f = Id
7. f o g = Id
8. EquivRel x,y:Alph*. x E y
9. x,y:Alph*. Dec(x E y)
10. h: n*n*
11. x,y:n*. (map(f;x) E map(f;y)) h(x) = h(y)
12. x:n*. map(f;x) E map(f;h(x))
13. x: Alph*
14. y: Alph*
15. (map(f o g;x) E map(f o g;y)) h(map(g;x)) = h(map(g;y))

(x E y) map(f;h(map(g;x))) = map(f;h(map(g;y)))
By: RWH (HypC 7) 15
Generated subgoal:

115. (map(Id;x) E map(Id;y)) h(map(g;x)) = h(map(g;y))
(x E y) map(f;h(map(g;x))) = map(f;h(map(g;y)))

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equallistapplyuniversefunctionpropnatural_numberall