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Proof step 11 from proof valid-eraseqp-invalidate (previous step)

apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, m0 < # apebs, valid-eraseq(apebs, q0), ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ valid-peb(apeb), (valid-peb(apebs[m, apeb][m0]) → avhdr.vol × avhdr.leb = apebs[m, apeb][m0].vidhdr.vol × apebs[m, apeb][m0].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m, apeb][m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m0 < # apebs, m < # apebs, valid-eraseq(apebs, q0), ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ valid-peb(apeb), (valid-peb(apebs[m, apeb][m0]) → avhdr.vol × avhdr.leb = avhdr0.vol × avhdr0.leb) ∧ valid-eraseq(apebs[m, apeb], 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[m, apeb][m0], aehdr0, avhdr0, buf0, m2, 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[m, apeb][m0], aehdr0, avhdr0, buf0, m2, boolvar0