Nuprl - Pf normalization_lemma 1 1 1 2 1 1 1 3 1 1 1 1 2 1

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At: normalization lemma 1 1 1 2 1 1 1 3 1 1 1 1 2 1

1. hyp: Formula List
2. concl: Formula List
3. fconcl.((f) > 0)
4. M: Formula List
5. N: Formula List
6. f: Formula
7. x1: Formula
8. x2: Formula
9. (x1x2) > 0
10. concl = (M @ (x1x2.N))
11. L: Sequent List
12. sL.((s) = 0)
13. sL.|= s |= < hyp,x1.(M @ N) >
14. a:Assignment. sL.a | s a | < hyp,x1.(M @ N) >
15. L1: Sequent List
16. sL1.((s) = 0)
17. sL1.|= s |= < hyp,x2.(M @ N) >
18. a:Assignment. sL1.a | s a | < hyp,x2.(M @ N) >
19. s(L @ L1).|= s
20. sL.|= s
21. sL1.|= s

|= < hyp,M @ (x1x2.N) >

By: BackThru Thm* hyp,M,N:Formula List, q,r:Formula. |= < hyp,q.(M @ N) > |= < hyp,r.(M @ N) > |= < hyp,M @ (qr.N) > THEN HypBackchain

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