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Proof step 97 from proof vols-is-max-is-min-eraseq (previous step)

# wlar0 = # wlar1, # apebs = # wlar1, apebs[m6] = mkpeb(aehdr0, avhdr0, buf0, m4, false), wlar1[m6] = wl-entry(m5, erasing), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m6] = wl-entry(m3, erasing), m6 < # wlar1, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar1, vols1, m0), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(v0, n2, mkpeb(aehdr0, avhdr0, buf0, m4, false)), valid-vtbl(apebs, vols1, wlar1, m0), valid-vtbl(apebs, vols0, wlar0, n0), valid-wl(apebs, wlar0), eq-entry(m6, lref) ∈ q1, m6 ∈ q0, eq-entry(m6, v0 × n2) ∈ q0, v0 ∈ vols0 ∧ n2 < # vols0[v0] → avhdr0.sqn ≠ valid-sqns(v0, n2, apebs).max, ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ avhdr0 = empty, v0 × n2 ∈ q1, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

User applied rule apply lemma

And obtained the following new goals

Proof step 98:
⊦ eq-entry(n, lref) ∈ q ∧ valid-eraseq(apebs, q) ∧ valid-peb(v, m, apebs[n]) → lref = v × m
Proof step 99:
# apebs = # wlar1, # wlar0 = # wlar1, wlar0[m6] = wl-entry(m3, erasing), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m6] = wl-entry(m5, erasing), apebs[m6] = mkpeb(aehdr0, avhdr0, buf0, m4, false), m6 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar1), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-ebatbl(apebs, wlar1, vols1, m0), valid-eraseq(apebs, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-peb(v0, n2, mkpeb(aehdr0, avhdr0, buf0, m4, false)), valid-vtbl(apebs, vols0, wlar0, n0), valid-vtbl(apebs, vols1, wlar1, m0), valid-wl(apebs, wlar0), eq-entry(m6, v0 × n2) ∈ q0, m6 ∈ q0, eq-entry(m6, lref) ∈ q1, v0 ∈ vols0 ∧ n2 < # vols0[v0] → avhdr0.sqn ≠ valid-sqns(v0, n2, apebs).max, eq-entry(m6, lref) ∈ q1 ∧ valid-eraseq(apebs, q1) ∧ valid-peb(v0, n2, apebs[m6]) → lref = v0 × n2, ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ avhdr0 = empty, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, v0 × n2 ∈ q1

Rule argument

spec: ubi-base name: in-valid-eraseqp-valid-lref seq: ⊦ eq-entry(n, lref) ∈ q ∧ valid-eraseq(apebs, q) ∧ valid-peb(v, m, apebs[n]) → lref = v × m subst: [n, lref, q, apebs, v, m] → [m6, lref, q1, apebs, v0, n2]

Additional information

Used terms: m6, lref, q1, apebs, v0, n2