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

x,y:Alph*. (x E y) map(f;h(map(g;x))) = map(f;h(map(g;y)))
By:
UnivCD
THEN
InstHyp [map(g;x);map(g;y)] 10
Generated subgoal:

112. x: Alph*
13. y: Alph*
14. (map(f;map(g;x)) E map(f;map(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)))

About:
alllistequalapplyuniversefunctionpropnatural_number