[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 191 from proof write-term (previous step)

# links(m, dirs) = files1[m].nlink, of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, files1[m].nlink, content0), dirs0 = dirs, err0 = ESUCCESS, ino0 = m2, ino1 = m0 + ino, n0 = ino, ino0 < ino1, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(m2, md0, files1[m].nlink, content0 upto m2)]), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, m ∈ files1, n ≤ # buf0 ⊦ ⟪afs_check_commit#(dirs, files1; err0; asynced); if err0 = ESUCCESS then afs_write_inode#(mkinode(m, md0, false, files1[m].nlink, 0, ino1); err0, dirs, files1; asynced); if err0 ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + n0⟫ (dirs0 = dirs), ino = 0, n = 0, m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 192:
# links(m, dirs) = files1[m].nlink, of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, files1[m].nlink, content0), err0 = ESUCCESS, ino ≠ 0, n ≠ 0, m2 < m0 + ino, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(m2, md0, files1[m].nlink, content0 upto m2)]), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, m ∈ files1, n ≤ # buf0 ⊦ ⟪afs_check_commit#(dirs, files1; err0; asynced); dirs0 := dirs; if err0 = ESUCCESS then afs_write_inode#(mkinode(m, md0, false, files1[m].nlink, 0, m0 + ino); err0, dirs, files1; asynced); if err0 ≠ ESUCCESS then ino := (m0 ≤ m2 ⊃ m2 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + ino⟫ (dirs0 = dirs), m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic