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Proof step 36 from proof valid-eraseq-stronger-prev-append-lref (previous step)

avhdr0.sqn = avhdr.sqn, apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m3] = mkpeb(aehdr0, avhdr0, buf0, m4, false), valid-sqns(v0, m2, apebs, m) = bag ++ apebs[m0].vidhdr.sqn ++ avhdr.sqn, (bag ++ apebs[m0].vidhdr.sqn ++ avhdr.sqn).max < (bag ++ apebs[m0].vidhdr.sqn).max, m3 < # apebs, m0 + 1 < # apebs, m < # apebs, m0 < m, m0 < # apebs, m3 < m, m3 + 1 < # apebs, (bag ++ apebs[m0].vidhdr.sqn ++ avhdr.sqn).max < avhdr.sqn, avhdr.sqn < (bag ++ apebs[m0].vidhdr.sqn).max, (bag ++ apebs[m0].vidhdr.sqn ++ avhdr.sqn).max + 1 < (bag ++ apebs[m0].vidhdr.sqn).max, valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m0, v0 × m2) '), valid-peb(v0, m2, mkpeb(aehdr0, avhdr0, buf0, m4, false)), valid-peb(v0, m2, apebs[m0]), valid-peb(v0, m2, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊦ m0 = m3, m0 ∈ q0, m3 ∈ q0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
avhdr0.sqn = avhdr.sqn, apebs[m3] = mkpeb(aehdr0, avhdr0, buf0, m4, false), apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m0] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar0), valid-sqns(v0, m2, apebs, m) = bag ++ avhdr1.sqn ++ avhdr.sqn, (bag ++ avhdr1.sqn ++ avhdr.sqn).max + 1 < (bag ++ avhdr1.sqn).max, avhdr.sqn < (bag ++ avhdr1.sqn).max, (bag ++ avhdr1.sqn ++ avhdr.sqn).max < avhdr.sqn, m3 + 1 < # apebs, m3 < m, m0 < # apebs, m0 < m, m < # apebs, m0 + 1 < # apebs, m3 < # apebs, (bag ++ avhdr1.sqn ++ avhdr.sqn).max < (bag ++ avhdr1.sqn).max, valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m0, v0 × m2) '), valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-peb(v0, m2, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v0, m2, apebs[m0]), valid-peb(v0, m2, mkpeb(aehdr0, avhdr0, buf0, m4, false)) ⊦ m0 = m3, m3 ∈ q0, m0 ∈ q0

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[m0], aehdr0, avhdr0, buf0, m4, boolvar0]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[m0], aehdr0, avhdr0, buf0, m4, boolvar0