Nuprl - Proof: ooc preserves dededkind inf 1 1

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At: ooc preserves dededkind inf 1 1

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

B
4. g : B

A
5. InvFuns(A;B;f;g)
6. a : A
7. h : A

A
8. Inj(A; A; h) &

(

x:A. h(x) = a)

a:B, f:(B

B). Inj(B; B; f) &

(

x:B. f(x) = a

By:	Witness: f(a) \| f o h o g

Generated subgoals:

1 8. Inj(A; A; h)
9. (x:A. h(x) = a)
Inj(B; B; f o h o g)
4 steps

2 8. Inj(A; A; h)
9. (x:A. h(x) = a)
(x:B. (f o h o g)(x) = f(a))
6 steps

About:

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1	8. Inj(A; A; h) 9. (x:A. h(x) = a) Inj(B; B; f o h o g)	4 steps
2	8. Inj(A; A; h) 9. (x:A. h(x) = a) (x:B. (f o h o g)(x) = f(a))	6 steps