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Proof step 33 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v0, m1, apebs, m).max, avhdr1.sqn = avhdr0.sqn, apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), wlar[n0] = wl-entry(m7, used), n0 + 1 < # wlar, m0 + 1 < # wlar, n0 < # wlar, m0 < m, avhdr0.sqn < avhdr.sqn, m < # wlar, m0 < # wlar, n0 < m, unique-elems(valid-sqns(v0, m1, apebs)), valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), m0 < m ∧ n0 < m ∧ m ≤ # apebs ∧ m0 ≠ n0 ∧ valid-peb(v0, m1, apebs[m0]) ∧ valid-peb(v0, m1, apebs[n0]) → (∃ bag. valid-sqns(v0, m1, apebs, m) = bag ++ apebs[m0].vidhdr.sqn ++ apebs[n0].vidhdr.sqn) ⊦ avhdr0.sqn = avhdr.sqn, n0 = m, n0 = m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
# apebs = # wlar, avhdr1.sqn = avhdr0.sqn, wlar[n0] = wl-entry(m7, used), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), valid-sqns(v0, m1, apebs, m) = bag ++ avhdr0.sqn ++ avhdr0.sqn, (bag ++ avhdr0.sqn ++ avhdr0.sqn).max < avhdr.sqn, n0 < m, m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, n0 + 1 < # wlar, (bag ++ avhdr0.sqn).max < avhdr.sqn, unique-elems(valid-sqns(v0, m1, apebs)), valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), (bag ++ avhdr0.sqn).max ≤ avhdr0.sqn ⊦ avhdr0.sqn = avhdr.sqn, n0 = m0, n0 = m

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ∅ ≠ bag ++ n; (s)% ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ m < n → m ≤ n; (s)