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Proof step 7 from proof refine-map (previous step)

# 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)

User applied rule insert program lemma

And obtained the following new goals

Proof step 8:
v ∈ avols, vtblpnum < # avols[v], vtblpnum0 + n ≤ LEB_SIZE, is-aligned(vtblpnum0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), n + n0 ≤ # buf, avols[v][vtblpnum].mapped? → vtblpnum0 ≥ avols[v][vtblpnum].fill, abs(avols, apebs, vols, q), ebm-cons(avols), ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum1, sqnum), vtblpnum2 = LEB_SIZE, vtblpnum3 = EB_PAGE_SIZE, ubi-io-inv(apebs) ⊦ ⟪ubi_write#(v, vtblpnum, vtblpnum0, n0, n, buf, vtblpnum3; vols, wlar, q, bflipset, vtblpnum1, sqnum, apebs; err)⟫ ⟨ebm_write#(v, vtblpnum, vtblpnum0, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0)
Proof step 9:
# apebs = # wlar, EB_PAGE_SIZE = EB_PAGE_SIZE, LEB_SIZE = LEB_SIZE, vols[v][vtblpnum2] = unmapped, avols0 = avols, buf0 = mkbuf(0), n1 = 0, n2 = 0, v0 = v, vtblpnum4 = vtblpnum2, vtblpnum5 = 0, vtblpnum6 = LEB_SIZE, vtblpnum7 = EB_PAGE_SIZE, vtblpnum2 < # vols[v], vtblpnum2 < # avols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(0, EB_PAGE_SIZE), ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum3, sqnum), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, 0 + 0 ≤ LEB_SIZE, 0 + 0 ≤ # mkbuf(0), avols[v][vtblpnum2].mapped? → 0 ≥ avols[v][vtblpnum2].fill ⊦ [ubi_write#(v, vtblpnum2, 0, 0, 0, mkbuf(0), EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum3, sqnum, apebs; err)] ( ⟨ebm_write#(v0, vtblpnum4, vtblpnum5, n2, n1, buf0; avols0; err0)⟩ (abs(avols0, apebs, vols, q) ∧ err = err0) → ⟨ebm_map#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0)), avols[v][vtblpnum2].mapped?, VTBL_VOLID ∈ vols

Rule argument

spec: <toplevel> name: refine-write seq: v ∈ avols, vtblpnum < # avols[v], vtblpnum0 + n ≤ LEB_SIZE, is-aligned(vtblpnum0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), n + n0 ≤ # buf, avols[v][vtblpnum].mapped? → vtblpnum0 ≥ avols[v][vtblpnum].fill, abs(avols, apebs, vols, q), ebm-cons(avols), ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum1, sqnum), vtblpnum2 = LEB_SIZE, vtblpnum3 = EB_PAGE_SIZE, ubi-io-inv(apebs) ⊦ ⟪ubi_write# (v, vtblpnum, vtblpnum0, n0, n, buf, vtblpnum3 ; vols, wlar, q, bflipset, vtblpnum1, sqnum, apebs ; err)⟫ ⟨ebm_write# (v, vtblpnum, vtblpnum0, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0) subst: [vtblpnum3, buf, n, n0, vtblpnum0, vtblpnum, v, apebs, sqnum, vtblpnum1, bflipset, q, wlar, vols, err, avols, vtblpnum2] → [EB_PAGE_SIZE, mkbuf(0), 0, 0, 0, vtblpnum2, v, apebs, sqnum, vtblpnum3, bflipset, q, wlar, vols, err, avols, LEB_SIZE] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ vols ∧ abs(avols, apebs, vols, q) → v ∈ avols; (ss)%⊦ v ∈ vols ∧ m < # vols[v] ∧ abs(avols, apebs, vols, q) → m < # avols[v]; (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 0 ≤ m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ # mkbuf(n) = n; (s)%⊦ ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ↔ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0); (s)