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Proof step 178 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err, dirs1, files1, asynced1)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md, false, m3, 0, m1) ∧ (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(m1, md, # links(m, dirs1), content0), files0[m] = mkfile(m1, md, # links(m, dirs1), content), files[m] = mkfile(m1, md, # links(m, dirs1), content1), buf-opt = none, err = ESUCCESS, content.stream from m1 = σ⊥, inode1 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, m1 < m0 + ino, m1 < m0, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ((content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to m1).buf = (content.stream to m1).buf, ino = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: append-to-ls seq: ⊦ ¬ # σ1 < ⌜n⌝ → σ1 + σ2 to n = σ1 to n subst: [n, σ2, σ1] → [m1, (⌜buf⌝ to ino) + (content.stream from m0 + ino), content.stream to m0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: m1, (⌜buf⌝ to ino) + (content.stream from m0 + ino), content.stream to m0