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Proof step 24 from proof vols-is-max-is-max-vols (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, v ∈ vols0 ↔ v ∈ vols1, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), to-vtbl(vols0)[v] = to-vtbl(vols1)[v], m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), 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, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), 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]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# vols0[v] = # vols1[v], # apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), m < # vols1[v], m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), 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, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-wl(apebs, wlar0), valid-wl(apebs, wlar1), v ∈ vols0, v ∈ vols1 ⊦ vols1[v][m] = unmapped, vols1[v][m] = vols0[v][m], VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ∈ vols → to-vtbl(vols)[v] = # vols[v]; (s)