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Proof step 16 from proof valid-wl-erasing-invalidate0 (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m0, apebs).max, wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), n < # wlar, m < # wlar, m < # apebs, valid-peb(v, m0, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)) ⊦ avhdr0.sqn = ( (valid-sqns(v, m0, apebs) \ (valid-peb(v, m0, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m2, false)) ⊃ {mkpeb(aehdr, avhdr, buf, m2, false).vidhdr.sqn} ;∅) ).max, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m0, apebs).max, wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), n < # wlar, m < # wlar, valid-peb(v, m0, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)) ⊦ avhdr0.sqn = (valid-sqns(v, m0, apebs) \ (valid-peb(v, m0, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅)).max, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

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)% ⊦ valid-peb(v, m, apeb) → valid-peb(apeb); (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)