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

PrintForm Definitions normalization Sections ClassicalProps(jlc) Doc

At: normalization lemma 1 1 1 2 1 1 1 3 1 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. ( < hyp,x1.(M @ N) > ) < ( < hyp,M @ (x1x2.N) > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < hyp,x1.(M @ N) > ) & (a:Assignment. sL.a | s a | < hyp,x1.(M @ N) > ))
12. ( < hyp,x2.(M @ N) > ) < ( < hyp,M @ (x1x2.N) > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < hyp,x2.(M @ N) > ) & (a:Assignment. sL.a | s a | < hyp,x2.(M @ N) > ))

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

By: RepeatFor 2 (Analyze -2 THENL [SequentRankReduce 0 THEN GenConclOnAps;Id])

Generated subgoal:

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

About: