Nuprl - Pf normalization_lemma 1 1 1 1 1 1 1 4 1 1

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At: normalization lemma 1 1 1 1 1 1 1 4 1 1

1. hyp: Formula List
2. concl: Formula List
3. fhyp.((f) > 0)
4. M: Formula List
5. N: Formula List
6. f: Formula
7. x1: Formula
8. x2: Formula
9. (x1x2) > 0
10. hyp = (M @ (x1x2.N))
11. ( < x1.(M @ N),concl > ) < ( < M @ (x1x2.N),concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < x1.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < x1.(M @ N),concl > ))
12. ( < x2.(M @ N),concl > ) < ( < M @ (x1x2.N),concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < x2.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < x2.(M @ N),concl > ))

L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ (x1x2.N),concl > ) & (a:Assignment. sL.a | s a | < M @ (x1x2.N),concl > )

By: Analyze -2

Generated subgoals:

1 11. ( < x2.(M @ N),concl > ) < ( < M @ (x1x2.N),concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < x2.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < x2.(M @ N),concl > ))
( < x1.(M @ N),concl > ) < ( < M @ (x1x2.N),concl > )

2 11. ( < x2.(M @ N),concl > ) < ( < M @ (x1x2.N),concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < x2.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < x2.(M @ N),concl > ))
12. L:Sequent List. sL.((s) = 0) & (sL.|= s |= < x1.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < x1.(M @ N),concl > )
L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ (x1x2.N),concl > ) & (a:Assignment. sL.a | s a | < M @ (x1x2.N),concl > )

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