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At: formula or left sound 1 1 2

1. concl: Formula List
2. M: Formula List
3. N: Formula List
4. q: Formula
5. r: Formula
6. |= < q.(M @ N),concl >
7. a: Full( < M @ (qr.N),concl > )
8. a |= < r.(M @ N),concl >

a |= < M @ (qr.N),concl >

By: Rewrite (UnfoldTopAbC THENC AbReduceC THENC HigherC (LemmaC Thm* P:(TProp), L,M:T List. x(L @ M).P(x) xL.P(x) xM.P(x)) THENC AbReduceC THENC HigherC (LemmaC Thm* a:Assignment, q,r:Formula. a | qr a | q & a | r)) 0

Generated subgoal:

1 FM.a | F a | q & a | r FN.a | F Fconcl.a |= F


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