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At: list quo choice pls 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1
1. q:
2. E: q*q*Prop
3. EquivRel x,y:q*. x E y
4. x,y:q*. Dec(x E y)
5. f: q*
6. g: q*
7. g o f = Id
8. f o g = Id
9. h:
10. n,k:. ((g(n)) E (g(k))) h(n) = h(k)
11. n:. (g(n)) E (g(h(n)))
12. x: q*
13. y: q*
14. (x E y) h(f(x)) = h(f(y))
15. (g o h o f)(x) = (g o h o f)(y)
16. (f o g o h o f)(x) = (f o g o h o f)(y)

h(f(x)) = h(f(y))
By: RWH (HypC 8) 16
Generated subgoal:

116. (Id o h o f)(x) = (Id o h o f)(y)
h(f(x)) = h(f(y))

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equalapplyfunctionlistnatural_numberpropall