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Proof step 41 from proof valid-wl-use (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m, apebs).max, apebs[n0] = mkpeb(aechdr(m3), avhdr1, buf1, m2, false), wlar[n0] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), n < # wlar, n0 < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m3), avhdr1, buf1, m2, false)), valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, v ≠ avhdr.vol ∨ m ≠ avhdr.leb ⊦ avhdr1.sqn = ((valid-sqns(v, m, apebs) -- avhdr0.sqn) ∪ ∅).max, n0 = n, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m, apebs).max, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), wlar[n0] = wl-entry(m3, used), apebs[n0] = mkpeb(aechdr(m3), avhdr1, buf1, m2, false), n0 < # wlar, n < # wlar, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0)), valid-peb(v, m, mkpeb(aechdr(m3), avhdr1, buf1, m2, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, v ≠ avhdr.vol ∨ m ≠ avhdr.leb ⊦ avhdr1.sqn = (valid-sqns(v, m, apebs) -- avhdr0.sqn).max, n0 = n, v = avhdr.vol ∧ m = avhdr.leb

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(apeb) → (valid-peb(v, m, apeb) ↔ v = apeb.vidhdr.vol ∧ m = apeb.vidhdr.leb); (ss)%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)