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Proof step 164 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, n0 ≤ # buf, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, ⌜buf⌝ to ino to n0 = ⌜buf⌝ to n0, #(⌜buf⌝ to ino) < ⌜n0⌝ , mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 165:
¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m
Proof step 166:
⟨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, 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, 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, n0 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, ⌜buf⌝ to ino to n0 = ⌜buf⌝ to n0, #(⌜buf⌝ to ino) < ⌜n0⌝ , mode ≠ MODE_W ∧ mode ≠ MODE_RW, ¬ # ⌜buf⌝ < ⌜ino⌝ ∧ n0 < ino

Rule argument

spec: stream, inst: buffer-inf name: to-to-ls seq: ¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m subst: [m, n, σ0] → [n0, ino, ⌜buf⌝ ] flags: <all paths>

Additional information

Used terms: n0, ino, ⌜buf⌝