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At: normalization lemma 1 1 1 1 1
1. hyp: Formula List
2. concl: Formula List
3. S:Sequent. (S) < ( < hyp,concl > ) (L:Sequent List. sL.((s) = 0) & (sL.|= s |= S ) & (a:Assignment. sL.a | s a | S))
4. fhyp.((f) > 0)
5. M,N:Formula List, f:Formula. (f) > 0 & hyp = (M @ (f.N))

L:Sequent List. sL.((s) = 0) & (sL.|= s |= < hyp,concl > ) & (a:Assignment. sL.a | s a | < hyp,concl > )
By:
Repeat (Analyze -1)
THEN
MoveToEnd 3
Generated subgoal:

13. fhyp.((f) > 0)
4. M: Formula List
5. N: Formula List
6. f: Formula
7. (f) > 0
8. hyp = (M @ (f.N))
9. S:Sequent. (S) < ( < hyp,concl > ) (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,concl > ) & (a:Assignment. sL.a | s a | < hyp,concl > )

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natural_numberimpliespairallless_thancons