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Proof step 5 from proof valid-eraseqp-update-other (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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