[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 68 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / 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].meta = files0[m].meta, files1[m].nlink = files0[m].nlink, files1[m].size = files0[m].size, files0[m] = mkfile(m2, md0, m3, content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), buf-opt = none, err = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), files1[m].content.stream to files1[m].size = files0[m].content.stream to files0[m].size, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files1, m ∈ files, n1 ≤ # buf, ino = 0 → files = files0, err0 = ESUCCESS ∨ ⌊err0⌋ , m ∈ files1 ∨ m ∈ files0 ⊦ [if ino ≠ 0 then err0 := ESUCCESS; of := of1; n := n1; if err0 = ESUCCESS then let ino3 = m1 in {n := ino, ino1 := of1[fd].pos + ino; if ino ≠ 0 ∧ ino3 < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files; err0; asynced1); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs0, files; asynced1)}; ino2 := of1[fd].pos; if err0 ≠ ESUCCESS then n := (ino2 ≤ ino3 ⊃ ino3 - ino2;0), err0 := ESUCCESS; of[fd].pos := ino2 + n}; file := of1[fd]] (err0 = ESUCCESS ⊃ (files[file.ino].content.stream to files[file.ino].size).buf = splice(buf, 0, (files1[file.ino].content.stream to files1[file.ino].size).buf, file.pos, n) ∧ of = of1[fd, file.pos:= (file.pos + n)] ∧ n ≤ n1 ∧ file.ino ∈ files1 ∧ file.ino ∈ files ∧ files[file.ino].meta = files1[file.ino].meta ∧ files -- file.ino = files1 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err0 = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err0⌋ ) ), n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
⟨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, 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, ino = 0 → files = files0, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ [if ino ≠ 0 then err0 := ESUCCESS; of := of1; n := n1; if err0 = ESUCCESS then let ino3 = m2 in {n := ino, ino1 := of1[fd].pos + ino; if ino ≠ 0 ∧ ino3 < ino1 then {inode0 := mkinode(m, md0, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files; err0; asynced1); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs0, files; asynced1)}; ino2 := of1[fd].pos; if err0 ≠ ESUCCESS then n := (ino2 ≤ ino3 ⊃ ino3 - ino2;0), err0 := ESUCCESS; of[fd].pos := ino2 + n}; file := of1[fd]] (err0 = ESUCCESS ⊃ (files[file.ino].content.stream to files[file.ino].size).buf = splice(buf, 0, (files1[file.ino].content.stream to files1[file.ino].size).buf, file.pos, n) ∧ of = of1[fd, file.pos:= (file.pos + n)] ∧ n ≤ n1 ∧ file.ino ∈ files1 ∧ file.ino ∈ files ∧ files[file.ino].meta = files1[file.ino].meta ∧ files -- file.ino = files1 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ;files ~ files1 ∧ of1 = of ∧ (err0 = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err0⌋ ) ), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)