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Proof step 30 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, avhdr0.sqn = ((valid-sqns(v, m5, apebs) \ ∅) ∪ (valid-peb(v, m5, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅)).max, wlar[n] = wl-entry(m4, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[m] = wl-entry(m2, used), apebs[n] = mkpeb(aechdr(m4), avhdr0, buf, m3, false), m < # wlar, n < # wlar, valid-peb(v, m5, mkpeb(aechdr(m4), avhdr0, buf, m3, false)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊦ avhdr0.sqn = valid-sqns(v, m5, apebs).max, n = m, valid-peb(v, m5, mkpeb(aehdr, avhdr, buf0, m0, boolvar0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# apebs = # wlar, avhdr0.sqn = (valid-sqns(v, m5, apebs) ∪ (valid-peb(v, m5, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅)).max, apebs[n] = mkpeb(aechdr(m4), avhdr0, buf, m3, false), wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[n] = wl-entry(m4, used), n < # wlar, m < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(v, m5, mkpeb(aechdr(m4), avhdr0, buf, m3, false)) ⊦ avhdr0.sqn = valid-sqns(v, m5, apebs).max, n = m, v = avhdr.vol ∧ m5 = 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)% ⊦ bag \ ∅ = bag; (s)