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

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At: normalization lemma 1 1 1 1 1 1 1 2 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. x: Formula
8. (x) > 0
9. hyp = (M @ (x.N))
10. ( < M @ N,x.concl > ) < ( < M @ (x.N),concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ N,x.concl > ) & (a:Assignment. sL.a | s a | < M @ N,x.concl > ))

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

By: Analyze -1

Generated subgoals:

1 ( < M @ N,x.concl > ) < ( < M @ (x.N),concl > )

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

About:

1	`( < M @ N,x.concl > ) < ( < M @ (x.N),concl > )`
2	10. `L:Sequent List. sL.((s) = 0) & (sL.\|= s \|= < M @ N,x.concl > ) & (a:Assignment. sL.a \| s a \| < M @ N,x.concl > )` `L:Sequent List. sL.((s) = 0) & (sL.\|= s \|= < M @ (x.N),concl > ) & (a:Assignment. sL.a \| s a \| < M @ (x.N),concl > )`