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Proof step 6 from proof refine-map (previous step)

# apebs = # wlar, vols[v][vtblpnum1] = unmapped, buf = mkbuf(0), vtblpnum = vtblpnum3, vtblpnum0 = EB_PAGE_SIZE, vtblpnum1 = vtblpnum2, vtblpnum2 < # avols[v], vtblpnum1 < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, v ∈ vols → v ∈ vols ∧ (vtblpnum1 < # vols[v] → vtblpnum1 < # vols[v] ∧ v ∈ vols) ⊦ ⟪ubi_write#(v, vtblpnum1, 0, 0, 0, buf, vtblpnum0; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)⟫ ⟨ebm_map#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0), avols[v][vtblpnum2].mapped?, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# apebs = # wlar, vols[v][vtblpnum2] = unmapped, vtblpnum2 < # avols[v], vtblpnum2 < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, ¬ avols[v][vtblpnum2].mapped?, ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_write#(v, vtblpnum2, 0, 0, 0, mkbuf(0), EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum3, sqnum, apebs; err)⟫ ⟨ebm_map#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%abs-vols-unmapped: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = unmapped ∧ abs(avols, apebs, vols, q) → ¬ avols[v][m].mapped?; (forward) from specification ubi-abs%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ v ∈ avols ∧ m < # avols[v] ∧ abs(avols, apebs, vols, q) → m < # vols[v]; (ss)% ⊦ v ∈ avols ∧ abs(avols, apebs, vols, q) → v ∈ vols; (ss)