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Proof step 24 from proof valid-sqns-write-h (previous step)

avhdr.sqn = avhdr0.sqn, apebs[m1] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), valid-sqns(v, m, apebs[n, apeb], m1) = (valid-sqns(v, m, apebs, m1) -- avhdr0.sqn) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅), n + 1 < # apebs, m1 < # apebs, n < m1, n < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) ⊦ valid-sqns(v, m, apebs[n, apeb], m1) ++ avhdr0.sqn = valid-sqns(v, m, apebs, m1) ∪ ∅, m1 = n, valid-peb(v, m, apeb)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
avhdr.sqn = avhdr0.sqn, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[m1] = mkpeb(aehdr, avhdr, buf, m0, boolvar), valid-sqns(v, m, apebs[n, apeb], m1) = valid-sqns(v, m, apebs, m1) -- avhdr0.sqn, n < # apebs, n < m1, m1 < # apebs, n + 1 < # apebs, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ⊦ valid-sqns(v, m, apebs[n, apeb], m1) ++ avhdr0.sqn = valid-sqns(v, m, apebs, m1), m1 = n, valid-peb(v, m, apeb)

Rule argument

Additional information

Used simplifier rules: union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]% ⊦ ∅ ∪ bag0 = bag0; (s)