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Proof step 5 from proof valid-eraseqp-invalidate (previous step)

m < # apebs, eqent.pnum < # apebs, valid-eraseq(apebs, q0), valid-peb(apebs[eqent.pnum]) → eqent.lebref = apebs[eqent.pnum].vidhdr.vol × apebs[eqent.pnum].vidhdr.leb, ∀ 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][eqent.pnum]) → eqent.lebref = apebs[m, apeb][eqent.pnum].vidhdr.vol × apebs[m, apeb][eqent.pnum].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
eqent = eq-entry(m0, lref), m0 < # apebs, m < # apebs, valid-eraseq(apebs, q0), valid-peb(apebs[m0]) → lref = apebs[m0].vidhdr.vol × apebs[m0].vidhdr.leb, ∀ 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]) → lref = apebs[m, apeb][m0].vidhdr.vol × apebs[m, apeb][m0].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0)

Rule argument

spec: erasequeueentry name: elim seq: ⊦ m = eqent.pnum ∧ lref = eqent.lebref ↔ eqent = eq-entry(m, lref) subst: [eqent, m, lref] → [eqent, m0, lref]

Additional information

Used simplifier rules: ⊦ m = eqent.pnum ∧ lref = eqent.lebref ↔ eqent = eq-entry(m, lref); (elim) Used terms: eqent, m0, lref