Nuprl - Proof: partition type 1 1 2 1 1 1 1 1 1 1

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At: partition type 1 1 2 1 1 1 1 1 1 1

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

Prop
4.

x:A.

!y:B. P(x;y)
5. f : A

B
6.

x:A. P(x;f(x))
7. y : B
8. u1 : A
9. P(u1;y)
10. y1 : B
11. y1 is the y:B. P(u1;y)
12. P(u1;f(u1))

<f(u1),u1> = <y,u1>

y:B

{x:A| P(x;y) }

By:	FwdThru: Hyp:11 on [ P(u1;y) ] THEN FwdThru: Hyp:11 on [ P(u1;f(u1)) ]

Generated subgoal:

1 13. y = y1
14. f(u1) = y1
<f(u1),u1> = <y,u1> y:B{x:A| P(x;y) }
1 step

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