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Proof step 24 from proof valid-wl-erasing-invalidate (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m1, apebs).max, apebs[n] = mkpeb(aechdr(m5), avhdr1, buf1, m4, false), wlar[n] = wl-entry(m5, used), wlar[m] = wl-entry(m0, erasing), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), m < # wlar, n < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr1, buf1, m4, false)), valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar)), n < # apebs ∧ m < # apebs ∧ n ≠ m ∧ valid-peb(v, m1, apebs[n]) ∧ valid-peb(v, m1, apebs[m]) → (∃ bag. valid-sqns(v, m1, apebs) = bag ++ apebs[n].vidhdr.sqn ++ apebs[m].vidhdr.sqn) ⊦ avhdr1.sqn = (valid-sqns(v, m1, apebs) -- avhdr0.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 25:
# apebs = # wlar, avhdr1.sqn = (bag ++ avhdr1.sqn ++ avhdr0.sqn).max, apebs[n] = mkpeb(aechdr(m5), avhdr1, buf1, m4, false), wlar[n] = wl-entry(m5, used), wlar[m] = wl-entry(m0, erasing), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), valid-sqns(v, m1, apebs) = bag ++ avhdr1.sqn ++ avhdr0.sqn, avhdr1.sqn < bag.max, m < # wlar, n < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr1, buf1, m4, false)), valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar)) ⊦ bag = ∅, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)% ⊦ (bag0 ++ n) -- n0 = (n = n0 ⊃ bag0;(bag0 -- n0) ++ n); (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)