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Proof step 265 from proof write-prepost-partial (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, files1[m] = mkfile(m2, md0, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs), content), buf-opt = none, err = ESUCCESS, content.stream from m2 = σ⊥, ino2 = of1[fd].pos, inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs), 0, m2), n = ino, 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), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ino = 0, n1 = 0, m2 < of1[fd].pos + ino, (err = ESUCCESS ⊃ (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content0.stream to m2).buf, m0, n) ∧ of1[fd, of1[fd].pos:= (ino2 + n)] = of1[fd, of1[fd].pos:= (m0 + n)] ∧ n ≤ n1 ∧ m ∈ files ∧ files[m].meta = md0 ∧ files -- m = files1 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW) ; files ~ files1 ∧ of1 = of1[fd, of1[fd].pos:= (ino2 + n)] ∧ ( err = EBADFD ∧ ( fd ∈ of1[fd, of1[fd].pos:= (ino2 + n)] → of1[fd, of1[fd].pos:= (ino2 + n)][fd].mode ≠ MODE_W ∧ of1[fd, of1[fd].pos:= (ino2 + n)][fd].mode ≠ MODE_RW) ∨ ⌊err⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 266:
⊦ write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1
Proof step 267:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1
Proof step 268:
⟨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, files1[m] = mkfile(m2, md0, # links(m, dirs), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs), content), buf-opt = none, err = ESUCCESS, content.stream from m2 = σ⊥, inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs), 0, m2), content0.stream to m2 = content.stream to m2, ino ≠ 0, n1 ≠ 0, 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), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs), 0, m2), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, m0 + ino ≤ m2, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW, (files[m].content.stream to files[m].size).buf = splice(buf, 0, (content.stream to m2).buf, m0, ino) ∧ files[m].meta = md0 ∧ files -- m = files0 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW)

Rule argument

Additional information

Used simplifier rules: write-inv-ls: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1;%write-inv-in0: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1;% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)% ⊦ mkfile(m, mode, m0).pos = m0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)