Nuprl - Proof: inv pair functionality wrt one one corr 1 1 3 1 1

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At: inv pair functionality wrt one one corr 1 1 3 1 1

1. A : Type
2. A' : Type
3. B : Type
4. B' : Type
5. f : A

A'
6. g : A'

A
7.

x:A. g(f(x)) = x
8.

y:A'. f(g(y)) = y
9. f' : B

B'
10. g' : B'

B
11.

x:B. g'(f'(x)) = x
12.

y:B'. f'(g'(y)) = y
13. (

de.de/d,e. <f' o d o g,f o e o g'>)

B'
14. (

de.de/d,e. <g' o d o f,g o e o f'>)

(A'

B')

B
15. d : A

B
16. e : B

A
17.

x:A. e(d(x)) = x
18.

y:B. d(e(y)) = y

<g' o f' o d o g o f,g o f o e o g' o f'> = <d,e>

By:	(2 Times Analyze) THEN (FunExtensionality (THEN (Reduce 0 (THEN (2 Times Rewrite by Hyp:18 \| Hyp:17 \| Hyp:12 \| Hyp:11 \| Hyp:8 \| Hyp:7)

Generated subgoal:

1 <g' o f' o d o g o f,g o f o e o g' o f'>/f,g. InvFuns(A;B;f;g)
1 step

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