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Proof step 7 from proof valid-eraseqp-append (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), eqent.pnum < # apebs, valid-eraseq(apebs, q0), valid-peb(apebs[eqent.pnum]) → eqent.lebref = apebs[eqent.pnum].vidhdr.vol × apebs[eqent.pnum].vidhdr.leb, ∀ apebs, n, aehdr, avhdr, buf, m, boolvar, lref. apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ valid-eraseq(apebs, q0) → ( valid-eraseq(apebs, q0 + eq-entry(n, lref) ') ↔ n < # apebs ∧ (valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)) → lref = avhdr.vol × avhdr.leb)) ⊦ valid-eraseq(apebs, q0 + eq-entry(n, lref) ') ↔ n < # apebs ∧ (valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)) → lref = avhdr.vol × avhdr.leb)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), eqent = eq-entry(m0, lref0), m0 < # apebs, valid-eraseq(apebs, q0), valid-peb(apebs[m0]) → lref0 = apebs[m0].vidhdr.vol × apebs[m0].vidhdr.leb, ∀ apebs, n, aehdr, avhdr, buf, m, boolvar, lref. apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ valid-eraseq(apebs, q0) → ( valid-eraseq(apebs, q0 + eq-entry(n, lref) ') ↔ n < # apebs ∧ (valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)) → lref = avhdr.vol × avhdr.leb)) ⊦ valid-eraseq(apebs, q0 + eq-entry(n, lref) ') ↔ n < # apebs ∧ (valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)) → lref = avhdr.vol × avhdr.leb)

Rule argument

spec: erasequeueentry name: elim seq: ⊦ m = eqent.pnum ∧ lref = eqent.lebref ↔ eqent = eq-entry(m, lref) subst: [eqent, m, lref] → [eqent, m0, lref0]

Additional information

Used simplifier rules: ⊦ m = eqent.pnum ∧ lref = eqent.lebref ↔ eqent = eq-entry(m, lref); (elim) Used terms: eqent, m0, lref0