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

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At: normalization lemma 1 1 1 2 1 1 1 3 1 1 1 1 3 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. a: Assignment
20. s(L @ L1).a | s

a | < hyp,x1.(M @ N) > a | < hyp,x2.(M @ N) >

By: FwdThru Thm* P:(TProp), L,M:T List. x(L @ M).P(x) xL.P(x) xM.P(x) [-1] THEN Analyze -1

Generated subgoals:

1 21. sL.a | s
a | < hyp,x1.(M @ N) > a | < hyp,x2.(M @ N) >

2 21. sL1.a | s
a | < hyp,x1.(M @ N) > a | < hyp,x2.(M @ N) >

About:

1	21. `sL.a \| s` `a \| < hyp,x1.(M @ N) > a \| < hyp,x2.(M @ N) >`
2	21. `sL1.a \| s` `a \| < hyp,x1.(M @ N) > a \| < hyp,x2.(M @ N) >`