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Proof step 4 from proof refine-write (previous step)

avols[default-volid][m2] = mapped(buf0, n1), avol = abs(avols[default-volid]), m = m1, m0 = m2, v = default-volid, m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, n1 ≤ m1, m1 + n ≤ LEB_SIZE, n0 + n ≤ # buf ⊦ ⟪if m0 < # avols[v] ∧ m + n ≤ LEB_SIZE ∧ is-aligned(m, EB_PAGE_SIZE) ∧ is-aligned(n, EB_PAGE_SIZE) ∧ n + n0 ≤ # buf ∧ (avols[v][m0].mapped? → m ≥ avols[v][m0].fill) then ebm_write#(v, m0, m, n0, n, buf; avols; err) else abort⟫ ⟨ebm_avol_write#(m2, m1, n0, n, buf; avol; err0)⟩ (avol = abs(avols[default-volid]) ∧ err = err0)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 5:
avols[default-volid][m2] = mapped(buf0, n1), avol = abs(avols[default-volid]), m = m1, m0 = m2, v = default-volid, m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), default-volid ∈ avols, n0 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n1 ≤ m1 ⊦ ⟪ebm_write#(v, m0, m, n0, n, buf; avols; err)⟫ ⟨ebm_avol_write#(m2, m1, n0, n, buf; avol; err0)⟩ (avol = abs(avols[default-volid]) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mapped(buf, m).mapped?; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mapped(buf, m).fill = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)