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At: normalization lemma 1 1 1 2 1 1 1 4
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. S:Sequent. (S) < ( < hyp,M @ (x1x2.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 @ (x1x2.N) > ) & (a:Assignment. sL.a | s a | < hyp,M @ (x1x2.N) > )
By: With < hyp,[x1; x2/ M @ N] > (Analyze -1)
Generated subgoal:

111. ( < hyp,[x1; x2/ M @ N] > ) < ( < hyp,M @ (x1x2.N) > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= < hyp,[x1; x2/ M @ N] > ) & (a:Assignment. sL.a | s a | < hyp,[x1; 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) > )

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existslistandequalintapply
natural_numberimpliespairconsallless_than