[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 608 from proof inv-write (previous step)

files0[m] = mkfile(m1, md, # links(m, dirs0), content0), of[fd] = mkfile(m, mode, m0), dirs = dirs0[ino, dirs0[ino].meta:= inode.meta], dirs1 = dirs0, err = ESUCCESS, files = files0[m, mkfile(m1, md, # links(m, dirs0), content0 upto m1)], ino = inode.ino, ino4 = 0, inode = mkinode(m, md, false, # links(m, dirs0), 0, m1), inode0 = (inode1.ino ∈ dirs ⊃ mkinode(inode1.ino, dirs[inode1.ino].meta, true, dirs[inode1.ino].nlink, dirs[inode1.ino].nsubdirs, dirs[inode1.ino].size) ;mkinode(inode1.ino, files[inode1.ino].meta, false, files[inode1.ino].nlink, 0, files[inode1.ino].size) ), inode1 = mkinode(m, md, false, # links(m, dirs0), 0, m1), dom of < ino3, afs-cons(dirs0, files0), of-cons(of, dirs0, files0), ino ∈ dirs0, fd ∈ of, m ∈ files0, n0 ≤ # buf0 ⊦ [vfs_write_loop#(m0, inode0, m0 + n0, buf0, dirs; ino4, err, files, asynced); if ino4 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode0.size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode0.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), n0 = 0, ino ∈ files, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)