Nuprl - Proof: bij imp exists inv2 1

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At: bij imp exists inv2 1

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

B
4.

a1,a2:A. f(a1) = f(a2)

a1 = a2
5.

b:B.

a:A. f(a) = b

g:(B

A). (

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

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

By:	DescribeFun: g by b:B. !a:A. f(a) = b THEN Witness: g

Generated subgoals:

1 b:B. !a:A. f(a) = b
3 steps

2 6. b:B. !a:A. f(a) = b
7. g : BA
8. b:B. f(g(b)) = b
(x:A. g(f(x)) = x) & (y:B. f(g(y)) = y)
3 steps

About:

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1	b:B. !a:A. f(a) = b	3 steps
2	6. b:B. !a:A. f(a) = b 7. g : BA 8. b:B. f(g(b)) = b (x:A. g(f(x)) = x) & (y:B. f(g(y)) = y)	3 steps