Nuprl - Pf normalization_lemma 1 1 1 1 1 1 1 5 1 1 2 2

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At: normalization lemma 1 1 1 1 1 1 1 5 1 1 2 2

1. hyp: Formula List
2. concl: Formula List
3. fhyp.((f) > 0)
4. M: Formula List
5. N: Formula List
6. f: Formula
7. y1: Formula
8. y2: Formula
9. (y1y2) > 0
10. hyp = (M @ (y1y2.N))
11. L:Sequent List. sL.((s) = 0) & (sL.|= s |= < y2.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < y2.(M @ N),concl > )
12. L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ N,y1.concl > ) & (a:Assignment. sL.a | s a | < M @ N,y1.concl > )

L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ (y1y2.N),concl > ) & (a:Assignment. sL.a | s a | < M @ (y1y2.N),concl > )

By: Repeat (Analyze -2) THEN Repeat (Analyze -1)

Generated subgoal:

1 11. L: Sequent List
12. sL.((s) = 0)
13. sL.|= s |= < y2.(M @ N),concl >
14. a:Assignment. sL.a | s a | < y2.(M @ N),concl >
15. L1: Sequent List
16. sL1.((s) = 0)
17. sL1.|= s |= < M @ N,y1.concl >
18. a:Assignment. sL1.a | s a | < M @ N,y1.concl >
L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ (y1y2.N),concl > ) & (a:Assignment. sL.a | s a | < M @ (y1y2.N),concl > )

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