Nuprl - Proof: one one corr fams sym 1 1 1 3

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At: one one corr fams sym 1 1 1 3

1. A : Type
2. A' : Type
3. B : A

Type
4. B' : A'

Type
5. f : A

A'
6. g : A'

A
7. F : x:A

B(x)

B'(f(x))
8. G : x:A

B'(f(x))

B(x)
9. InvFuns(A;A';f;g)
10.

u:A. InvFuns(B(u);B'(f(u));F(u);G(u))
11. G o g

x':A'

B'(x')

B(g(x'))
12. F o g

x':A'

B(g(x'))

B'(x')

F:(x':A'

B'(x')

B(g(x'))), G:(x':A'

B(g(x'))

B'(x')).

InvFuns(A';A;g;f) & (

u:A'. InvFuns(B'(u);B(g(u));F(u);G(u)))

By:	Witness: G o g \| F o g

Generated subgoals:

1 InvFuns(A';A;g;f)
1 step

2 13. u : A'
InvFuns(B'(u);B(g(u));(G o g)(u);(F o g)(u))
5 steps

About:

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1	InvFuns(A';A;g;f)	1 step
2	13. u : A' InvFuns(B'(u);B(g(u));(G o g)(u);(F o g)(u))	5 steps