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Proof step 294 from proof write-prepost (previous step)

⟨afs_truncate#(m2, m2 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files0[m] = mkfile(m2, md0, # links(m, dirs), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m2, md0, # links(m, dirs), content0), buf-opt = none, err = ESUCCESS, err0 = ESUCCESS, content.stream from m2 = σ⊥, ino2 = of1[fd].pos, ino3 = m2, inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs), 0, m2), n = 0, n0 = n1, of = of1, content0.stream to m2 = content.stream to m2, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of, m ∈ files1, fd ∈ of1, n1 ≤ # buf, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ [file := of1[fd]] (err0 = ESUCCESS ⊃ (files0[file.ino].content.stream to files0[file.ino].size).buf = splice(buf, 0, (files1[file.ino].content.stream to files1[file.ino].size).buf, file.pos, n) ∧ of[fd, of[fd].pos:= (ino2 + n)] = of1[fd, file.pos:= (file.pos + n)] ∧ n ≤ n1 ∧ file.ino ∈ files1 ∧ file.ino ∈ files0 ∧ files0[file.ino].meta = files1[file.ino].meta ∧ files0 -- file.ino = files1 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ; of1 = of[fd, of[fd].pos:= (ino2 + n)] ∧ (err0 = EBADFD ∧ (fd ∈ of[fd, of[fd].pos:= (ino2 + n)] → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err0⌋ ) ), n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 295:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0

Rule argument

Additional information

Used simplifier rules: write-inv-in1: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0;% ⊦ splice(buf, n0, buf0, n1, 0) = buf0; (s)% ⊦ 0 ≤ m; (s)% ⊦ mkfile(m, mode, m0).ino = m; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, mode, m0).mode = mode; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)