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Proof step 2 from proof refine-write (previous step)

avol = abs(avols[v]), v = default-volid, avol[m].mapped?, m < # avol, ebm-cons(avols), ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), v ∈ avols, n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # avol[m].data ≤ m0 ⊦ ⟪ebm_vol_write#(m, m0, n0, n, buf, v; avols; err)⟫ ⟨ebm_avol_write#(m, m0, n0, n, buf; avol; err0)⟩ (avol = abs(avols[v]) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
avols[default-volid][m] = mapped(buf0, n1), avol = abs(avols[default-volid]), m < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), default-volid ∈ avols, n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, n1 ≤ m0 ⊦ ⟪ebm_vol_write#(m, m0, n0, n, buf, default-volid; avols; err)⟫ ⟨ebm_avol_write#(m, m0, n0, n, buf; avol; err0)⟩ (avol = abs(avols[default-volid]) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ abs(mapped(buf, n)) = mapped(subarray(buf, 0, n)); (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ abs(leb).mapped? ↔ (∃ buf, n. leb = mapped(buf, n)); (s)% ⊦ n < # evol → abs(evol)[n] = abs(evol[n]); (s)% ⊦ # abs(evol) = # evol; (s)