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At: normalization lemma 1 1 1 2 1 1 1 5
1. hyp: Formula List
2. concl: Formula List
3. fconcl.((f) > 0)
4. M: Formula List
5. N: Formula List
6. f: Formula
7. y1: Formula
8. y2: Formula
9. (y1y2) > 0
10. concl = (M @ (y1y2.N))
11. S:Sequent. (S) < ( < hyp,M @ (y1y2.N) > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= S ) & (a:Assignment. sL.a | s a | S))

L:Sequent List. sL.((s) = 0) & (sL.|= s |= < hyp,M @ (y1y2.N) > ) & (a:Assignment. sL.a | s a | < hyp,M @ (y1y2.N) > )
By: With < y1.hyp,y2.(M @ N) > (Analyze -1)
Generated subgoal:

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

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existslistandequalintapply
natural_numberimpliespairconsallless_than