Nuprl - Proof: change-lemma 1 1 2 2 1 1 1 1 1 1 2 2 1 1 4 1 1

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At: change-lemma 1 1 2 2 1 1 1 1 1 1 2 2 1 1 4 1 1

1. es : ES
2. x : Id
3. i : Id
4. T : Type
5.

x,y:T. Dec(x = y)
6. vartype(i;x)

r T
7.

e:E. loc(e) = i

(x when e)

T
8.

e:E. loc(e) = i

(x after e)

T
9. WellFnd{i}(E;x,y.(x <loc y))
10. j : E
11.

k:E.
11. (k <loc j)
11.

11. (

e:E.
11. (e

k
11. (

11. (loc(k) = i
11. (

11. (

(

[e, k].

(x after ev) = (x when ev))

(x after k) = (x when e))
12. e : E
13. (e <loc j)
14. loc(j) = i
15. (x after j) = (x when j)
16. loc(e) = i
17.

first(j)
18. (x when j) = (x after pred(j))
19. ev : {e:E| loc(e) = i }
20. (ev

[e, pred(j)]) &

(x after ev) = (x when ev)

(ev

[e, j]) &

(x after ev) = (x when ev)

By:	ParallelOp -1

Generated subgoal:

1 20. (ev [e, pred(j)])
(ev [e, j])
10 steps

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