| # apebs = # wlar, v ∈ vols ↔ v ∈ avols, buf = buf0, vtblpnum < # avols[v], bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar), v ∈ avols, n0 + n ≤ # buf0, vtblpnum0 + n ≤ LEB_SIZE, v ∈ vols → # vols[v] = # avols[v] ∧ (∀ m. m < # vols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q)) ⊦ ⟪ubi_read#(v, vtblpnum, vtblpnum0, n0, n, vols, LEB_SIZE, apebs; buf, bflipset; err)⟫ ⟨ebm_read#(v, vtblpnum, vtblpnum0, n0, n, avols; buf0; err0)⟩ (buf = buf0 ∧ err = err0), VTBL_VOLID ∈ vols |
# vols[v] = # avols[v], # apebs = # wlar, buf = buf0, vtblpnum < # avols[v], bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, n0 + n ≤ # buf0, vtblpnum0 + n ≤ LEB_SIZE, ¬ VTBL_VOLID ∈ vols, ∀ m. m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ ⟪ubi_read#(v, vtblpnum, vtblpnum0, n0, n, vols, LEB_SIZE, apebs; buf, bflipset; err)⟫ ⟨ebm_read#(v, vtblpnum, vtblpnum0, n0, n, avols; buf0; err0)⟩ (buf = buf0 ∧ err = err0)
Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic