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Proof step 86 from proof synced-write-buf (previous step)

⟨fail_or_success#(; ; err)⟩ (err = err2), # lpt = # avol, true ↔ isbuf0, avol[m1] = mapped(buf0), avol[m, mapped(avol[m].data + subarray(buf, 0, n))] = avol1, bleb = buffered(m1), err2 = err1, ¬ isbuf, m = bleb.leb, m0 = m2, n0 = n2, bleb.isbuf?, avol[m].mapped?, m < # avol, m1 < # avol, n < n0, awbuf-inv(avol, buffered(m1)), is-aligned(# avol[m].data + n, EB_PAGE_SIZE), avol0 ↓ avol1, 0 + n ≤ # buf, # buf0 + n2 ≤ LEB_SIZE, n2 ≤ # buf, # avol[bleb.leb].data + n0 ≤ LEB_SIZE, n0 ≤ # buf, bleb ≠ nobuffer → avol[bleb.leb].mapped? ∧ bleb.leb < # avol ∧ bleb.isbuf?, n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; let m = buffered(m1).leb in if err = ESUCCESS then avol[m] := mapped(avol[m].data + subarray(buf, 0, n2)) else { choose n1 with n1 ≠ 0 ∧ n1 < n2 ∧ is-aligned(# avol[m].data + n1, EB_PAGE_SIZE) in avol[m] := mapped(avol[m].data + subarray(buf, 0, n1)) ifnone skip or skip; isbuf := true}⟩ (synced(avol) ∧ avol0 ↓ avol), bleb = nobuffer, err2 = ESUCCESS, n = 0, avol0 ↓ avol

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
⟨fail_or_success#(; ; err)⟩ (err = err2), # lpt = # avol, avol[m1] = mapped(buf0), err2 ≠ ESUCCESS, n ≠ 0, n < n2, m1 < # avol, n < # buf, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n, EB_PAGE_SIZE), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, # buf0 + n2 ≤ LEB_SIZE, n2 ≤ # buf ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; let m = buffered(m1).leb in if err = ESUCCESS then avol[m] := mapped(avol[m].data + subarray(buf, 0, n2)) else { choose n1 with n1 ≠ 0 ∧ n1 < n2 ∧ is-aligned(# avol[m].data + n1, EB_PAGE_SIZE) in avol[m] := mapped(avol[m].data + subarray(buf, 0, n1)) ifnone skip or skip; isbuf := true}⟩ (synced(avol) ∧ avol0 ↓ avol)

Rule argument

Additional information

Used simplifier rules: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)%⊦ (buf0 + buf1).align↓ = buf0.align↓ ↔ # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE; (s)% ⊦ mapped(buf0) ↓ mapped(buf1) ↔ buf0 = buf1.align↓; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n < # avol0 ⊦ avol1 ↓ avol0[n, mapped(buf)] → avol1[n] = mapped(buf.align↓); (s)%n < # avol0 ⊦ avol1 ↓ avol0[n, aleb] → (avol1 ↓ avol0 ↔ avol1[n] ↓ avol0[n]); (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ buffered(m).isbuf?; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ nobuffer ≠ buffered(m); (s)