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Proof step 11 from proof valid-eraseq-strong-imp-p (previous step)

apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, vtbl, q0), ∀ v, m. (valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ↔ lref = v × m) ∧ (lref = v × m ∧ v ∈ vtbl ∧ m < vtbl[v] → avhdr.sqn ≠ valid-sqns(v, m, apebs).max) ⊦ valid-eraseq(apebs, eq-entry(m0, lref) ' + q0), m0 ∈ q0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ valid-eraseq(apebs, eqent ' + q) ↔ eqent.pnum < # apebs ∧ (valid-peb(apebs[eqent.pnum]) → eqent.lebref = apebs[eqent.pnum].vidhdr.vol × apebs[eqent.pnum].vidhdr.leb) ∧ valid-eraseq(apebs, q)
Proof step 13:
apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, vtbl, q0), ∀ v, m. (valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ↔ lref = v × m) ∧ (lref = v × m ∧ v ∈ vtbl ∧ m < vtbl[v] → avhdr.sqn ≠ valid-sqns(v, m, apebs).max) ⊦ m0 ∈ q0, eq-entry(m0, lref).pnum < # apebs ∧ ( valid-peb(apebs[eq-entry(m0, lref).pnum]) → eq-entry(m0, lref).lebref = apebs[eq-entry(m0, lref).pnum].vidhdr.vol × apebs[eq-entry(m0, lref).pnum].vidhdr.leb) ∧ valid-eraseq(apebs, q0)

Rule argument

spec: ubi-base name: valid-eraseqp-rec seq: ⊦ valid-eraseq(apebs, eqent ' + q) ↔ eqent.pnum < # apebs ∧ ( valid-peb(apebs[eqent.pnum]) → eqent.lebref = apebs[eqent.pnum].vidhdr.vol × apebs[eqent.pnum].vidhdr.leb) ∧ valid-eraseq(apebs, q) subst: [q, eqent, apebs] → [q0, eq-entry(m0, lref), apebs] flags: <all paths>

Additional information

Used terms: q0, eq-entry(m0, lref), apebs