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Proof step 171 from proof write-prepost (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, files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), 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 ≠ 0, n1 ≠ 0, ⌜buf⌝ to ino to n0 ≠ ⌜buf⌝ to n0, # buf < ino, n0 < ino, n1 < 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 ∈ files, m ∈ files1, n0 ≤ # buf, n1 ≤ # buf, ⌊err0⌋ , ¬ #(⌜buf⌝ to ino) < ⌜n0⌝ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule apply lemma

And obtained the following new goals

Proof step 172:
⊦ write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1

Rule argument

spec: <toplevel> name: write-inv-ls seq: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1 subst: [n0, n1, ino, md, m, m1, m0, buf, n2, dirs, files0, files1] → [m0, n1, m, md, # links(m, dirs1), 0, n0 + m0, buf, ino, dirs0, files0, files]

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: m0, n1, m, md, # links(m, dirs1), 0, n0 + m0, buf, ino, dirs0, files0, files