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

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At: inv pair functionality wrt one one corr 1 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

(

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

By:	(Analyze THEN Analyze-1) THEN New:[d \| e] Analyze-2 THEN Reduce 0 THEN Reduce -1 THEN Analyze THEN Reduce Concl THEN Analyze-1

Generated subgoal:

1 13. d : AB
14. e : BA
15. x:A. e(d(x)) = x
16. y:B. d(e(y)) = y
InvFuns(A';B';f' o d o g;f o e o g')
1 step

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