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Proof step 9 from proof refine-map (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# 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_write#(v, vtblpnum2, 0, 0, 0, mkbuf(0); avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0) → ⟨ebm_map#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (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)% ⊦ 0 ≤ m; (s)% ⊦ # mkbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic