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Proof step 143 from proof write-prepost-partial (previous step)

⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err, dirs1, files1, asynced1)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md, false, m3, 0, n0 + m0) ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced1 ↔ asynced0)), # links(m, dirs1) = m3, files1 -- m = files0 -- m, of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files[m] = mkfile(n0 + m0, md, # links(m, dirs1), content1), buf-opt = none, err = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode1 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n0 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), files1 ~ files0, fd ∈ of1, m ∈ files1, m ∈ files, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, (content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0 = ⌜copy(buf, 0, (content.stream to n0 + m0).buf, m0, n0)⌝ , mode ≠ MODE_W ∧ mode ≠ MODE_RW, 0 + n0 ≤ # buf ∧ m0 + n0 ≤ # (content.stream to n0 + m0).buf

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 144:
⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err, dirs1, files1, asynced1)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md, false, m3, 0, n0 + m0) ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced1 ↔ asynced0)), # links(m, dirs1) = m3, files1 -- m = files0 -- m, files[m] = mkfile(n0 + m0, md, # links(m, dirs1), content1), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode1 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n1 ≠ 0, (content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0 ≠ ⌜copy(buf, 0, (content.stream to n0 + m0).buf, m0, n0)⌝ , # buf + 1 < ino, n0 < ino, # buf < n0, n1 < n0, # buf < ino, n1 < ino, n1 + 1 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ ⌜m⌝ .n = m; (s)%n∞ ≠ ∞ ⊦ (⌜m⌝ + n∞).n = m + n∞.n; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ # content.stream = ∞; (s)%finp(σ) ⊦ # σ.buf = (# σ).n; (s)% ⊦ finp(σ0 to m); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)