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

PrintForm Definitions normalization Sections ClassicalProps(jlc) Doc

At: normalization lemma 1 1 1 1 1 1 1 5 1 1 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. ( < M @ N,y1.concl > ) < ( < M @ (y1y2.N),concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < M @ N,y1.concl > ) & (a:Assignment. sL.a | s a | < M @ N,y1.concl > ))
12. L:Sequent List. sL.((s) = 0) & (sL.|= s |= < y2.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < y2.(M @ N),concl > )

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

By: Analyze -2

Generated subgoals:

1 11. L:Sequent List. sL.((s) = 0) & (sL.|= s |= < y2.(M @ N),concl > ) & (a:Assignment. sL.a | s a | < y2.(M @ N),concl > )
( < M @ N,y1.concl > ) < ( < M @ (y1y2.N),concl > )

2 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 > )

About:

1	11. `L:Sequent List. sL.((s) = 0) & (sL.\|= s \|= < y2.(M @ N),concl > ) & (a:Assignment. sL.a \| s a \| < y2.(M @ N),concl > )` `( < M @ N,y1.concl > ) < ( < M @ (y1y2.N),concl > )`
2	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 > )`