Nuprl - Proof: es-first-exists 1 2

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At: es-first-exists 1 2

1. es : ES
2. WellFnd{i}(E;x,y.(x <loc y))
3. j : E
4.

k:E. (k <loc j)

(

e:E. first(e) & e

k )
5.

first(j)

e:E. first(e) & e

By:	InstHyp [pred(j)] -2

Generated subgoals:

1   (pred(j) <loc j)
1 step

2 6. e:E. first(e) & e  pred(j)
  e:E. first(e) & e  j
4 steps

About:

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1	(pred(j) <loc j)	1 step
2	6. e:E. first(e) & e pred(j) e:E. first(e) & e j	4 steps