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Proof step 45 from proof valid-wl-use (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), wlar[n0] = wl-entry(m3, used), apebs[n0] = mkpeb(aechdr(m3), avhdr1, buf1, m2, false), valid-sqns(v, m, apebs) = bag ++ avhdr0.sqn ++ avhdr1.sqn, 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)), (bag ++ avhdr0.sqn).max ≤ avhdr1.sqn, 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 = (avhdr1.sqn = avhdr0.sqn ⊃ bag ++ avhdr0.sqn;bag ++ avhdr1.sqn).max, n0 = n, v = avhdr.vol ∧ m = avhdr.leb

Heuristic if-then-else split applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)% ⊦ bag ≠ ∅ → (bag ++ m).max = (bag.max > m ⊃ bag.max;m); (s)% ⊦ m > n ↔ n < m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ n < n; (s)