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Proof step 7 from proof vols-is-max-is-max-vols (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, 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(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-vtbl(apebs, vols0, wlar0, n0), valid-vtbl(apebs, vols1, wlar1, m0), valid-wl(apebs, wlar0), valid-wl(apebs, wlar1) ⊦ VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m]))

User applied rule apply lemma

And obtained the following new goals

Proof step 8:
⊦ ubi-cons(apebs, vols0, wlar0, q0, bflipset0, n0, n1) ∧ ubi-cons(apebs, vols1, wlar1, q1, bflipset1, m0, m1) → n0 = m0
Proof step 9:
# wlar0 = # wlar1, # apebs = # wlar1, apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), bflipset-cons(bflipset1, 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(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols1, wlar1, m0), valid-vtbl(apebs, vols0, wlar0, n0), valid-wl(apebs, wlar1), valid-wl(apebs, wlar0), ubi-cons(apebs, vols0, wlar0, q0, bflipset0, n0, n1) ∧ ubi-cons(apebs, vols1, wlar1, q1, bflipset1, m0, m1) → n0 = m0 ⊦ VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0, (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m]))

Rule argument

spec: <toplevel> name: ubi-cons-same-vtbl seq: ⊦ ubi-cons(apebs, vols0, wlar0, q0, bflipset0, n0, n1) ∧ ubi-cons(apebs, vols1, wlar1, q1, bflipset1, m0, m1) → n0 = m0 subst: [apebs, vols0, wlar0, q0, bflipset0, n0, n1, vols1, wlar1, q1, bflipset1, m0, m1] → [apebs, vols0, wlar0, q0, bflipset0, n0, n1, vols1, wlar1, q1, bflipset1, m0, m1]

Additional information

Used terms: apebs, vols0, wlar0, q0, bflipset0, n0, n1, vols1, wlar1, q1, bflipset1, m0, m1