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Proof step 9 from proof valid-eraseqp-valid-lebref (previous step)

apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, valid-eraseq(apebs, q0), valid-peb(v, m, apebs[n]), n ∈ eq-entry(m0, lref) ' + q0, valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) → lref = avhdr.vol × avhdr.leb, ∀ apebs, v, m, n. valid-eraseq(apebs, q0) ∧ valid-peb(v, m, apebs[n]) ∧ n ∈ q0 → eq-entry(n, v × m) ∈ q0 ⊦ eq-entry(n, v × m) = eq-entry(m0, lref), eq-entry(n, v × m) ∈ q0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n ∈ q0 + q1 ↔ n ∈ q0 ∨ n ∈ q1
Proof step 11:
apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, valid-eraseq(apebs, q0), valid-peb(v, m, apebs[n]), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) → lref = avhdr.vol × avhdr.leb, ∀ apebs, v, m, n. valid-eraseq(apebs, q0) ∧ valid-peb(v, m, apebs[n]) ∧ n ∈ q0 → eq-entry(n, v × m) ∈ q0, n ∈ eq-entry(m0, lref) ' ∨ n ∈ q0 ⊦ eq-entry(n, v × m) = eq-entry(m0, lref), eq-entry(n, v × m) ∈ q0

Rule argument

spec: erasequeue name: in-concat seq: ⊦ n ∈ q0 + q1 ↔ n ∈ q0 ∨ n ∈ q1 subst: [q1, q0, n] → [q0, eq-entry(m0, lref) ', n] flags: <all paths>

Additional information

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