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At: list quo choice pls 1 1 1 2 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)) & (n:. (g(n)) E (g(h(n))))

(x,y:q*. (x E y) (g o h o f)(x) = (g o h o f)(y)) & (x:q*. x E ((g o h o f)(x)))
By:
Analyze 10
THEN
Analyze 0
Generated subgoals:

110. n,k:. ((g(n)) E (g(k))) h(n) = h(k)
11. n:. (g(n)) E (g(h(n)))
x,y:q*. (x E y) (g o h o f)(x) = (g o h o f)(y)
210. n,k:. ((g(n)) E (g(k))) h(n) = h(k)
11. n:. (g(n)) E (g(h(n)))
x:q*. x E ((g o h o f)(x))

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andalllistnatural_numberequalapplyfunctionprop