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Proof step 23 from proof valid-wl-erasing-invalidate0 (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m0, apebs).max, apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), wlar[n] = wl-entry(m5, used), apebs[m] = mkpeb(aehdr0, avhdr1, buf1, m1, boolvar), m < # wlar, n < # wlar, valid-peb(v, m0, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)), valid-peb(v, m0, mkpeb(aehdr0, avhdr1, buf1, m1, boolvar)), m < # apebs ∧ n < # apebs ∧ m ≠ n ∧ valid-peb(v, m0, apebs[m]) ∧ valid-peb(v, m0, apebs[n]) → (∃ bag. valid-sqns(v, m0, apebs) = bag ++ apebs[m].vidhdr.sqn ++ apebs[n].vidhdr.sqn) ⊦ avhdr0.sqn = (valid-sqns(v, m0, apebs) -- avhdr1.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 24:
# apebs = # wlar, apebs[m] = mkpeb(aehdr0, avhdr1, buf1, m1, boolvar), wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), valid-sqns(v, m0, apebs) = bag ++ avhdr1.sqn ++ avhdr0.sqn, n < # wlar, m < # wlar, valid-peb(v, m0, mkpeb(aehdr0, avhdr1, buf1, m1, boolvar)), valid-peb(v, m0, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)), (bag ++ avhdr1.sqn).max ≤ avhdr0.sqn ⊦ avhdr0.sqn = (avhdr0.sqn = avhdr1.sqn ⊃ bag ++ avhdr1.sqn;bag ++ avhdr0.sqn).max, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ (bag0 ++ n) -- n0 = (n = n0 ⊃ bag0;(bag0 -- n0) ++ n); (s)% ⊦ ∅ ≠ bag ++ n; (s)% ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)