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At: fin alph list quo 1 1 1 1 1 3 1 1 1 1 2 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: Alph*
12. map(f;map(g;x)) E map(f;h(map(g;x)))

x E map(f;h(map(g;x)))
By:
RWH (LemmaC Thm* f:(AB), g:(BC), as:A*. map(g;map(f;as)) = map(g o f;as)) 12
THEN
Analyze 6
Generated subgoal:

16. 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: Alph*
13. map(f o g;x) E map(f;h(map(g;x)))
x E map(f;h(map(g;x)))

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applyuniversefunctionlistpropnatural_numberallequal