[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 195 from proof write-prepost (previous step)

⟨afs_truncate#(m2, m2 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files1[m] = mkfile(m2, md0, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs1), content), buf-opt = none, err2 = ESUCCESS, content.stream from m2 = σ⊥, ino2 = of1[fd].pos, inode = mkinode(m, md0, false, # links(m, dirs1), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs1), 0, m2), n = ino, content0.stream to m2 = content.stream to m2, m2 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs1), 0, m2), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs1), 0, m2), buf, ino, dirs0, files0, files), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, (ino2 ≤ m2 ⊃ m2 ≥ ino2;true), ⌊err0⌋ ∨ err0 = ESUCCESS, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ err0 = ESUCCESS, ino = 0, n1 = 0, (ESUCCESS = ESUCCESS ⊃ (files[of1[fd].ino].content.stream to files[of1[fd].ino].size).buf = splice(buf, 0, (files1[of1[fd].ino].content.stream to files1[of1[fd].ino].size).buf, of1[fd].pos, (ino2 ≤ m2 ⊃ m2 - ino2;0)) ∧ of1[fd, of1[fd].pos:= (ino2 + (ino2 ≤ m2 ⊃ m2 - ino2;0))] = of1[fd, of1[fd].pos:= (of1[fd].pos + (ino2 ≤ m2 ⊃ m2 - ino2;0))] ∧ (ino2 ≤ m2 ⊃ m2 - ino2;0) ≤ n1 ∧ of1[fd].ino ∈ files1 ∧ of1[fd].ino ∈ files ∧ files[of1[fd].ino].meta = files1[of1[fd].ino].meta ∧ files -- of1[fd].ino = files1 -- of1[fd].ino ∧ (of1[fd].mode = MODE_W ∨ of1[fd].mode = MODE_RW) ; files ~ files1 ∧ of1 = of1[fd, of1[fd].pos:= (ino2 + (ino2 ≤ m2 ⊃ m2 - ino2;0))] ∧ ( ESUCCESS = EBADFD ∧ (fd ∈ of1[fd, of1[fd].pos:= (ino2 + (ino2 ≤ m2 ⊃ m2 - ino2;0))] → of1[fd].mode ≠ MODE_W ∧ of1[fd].mode ≠ MODE_RW) ∨ ⌊ESUCCESS⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 196:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1
Proof step 197:
⟨afs_truncate#(m2, m2 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files0[m] = mkfile(m2, md0, # links(m, dirs1), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m2, md0, # links(m, dirs1), content0), buf-opt = none, err2 = ESUCCESS, content.stream from m2 = σ⊥, inode = mkinode(m, md0, false, # links(m, dirs1), 0, m2), inode0 = mkinode(m, md0, false, # links(m, dirs1), 0, m2), content0.stream to m2 = content.stream to m2, ino ≠ 0, n1 ≠ 0, m2 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs1), 0, m2), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md0, false, # links(m, dirs1), 0, m2), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, ⌊err0⌋ , 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, (m0 ≤ m2 ⊃ m2 - m0;0)) ∧ (m0 ≤ m2 ⊃ m2 - m0;0) ≤ n1 ∧ files[m].meta = md0 ∧ files -- m = files0 -- m ∧ (mode = MODE_W ∨ mode = MODE_RW)

Rule argument

Additional information

Used simplifier rules: write-inv-in0: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1;% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, mode, m0).mode = mode; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, mode, m0).pos = m0; (s)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)