[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 365 from proof inv-write (previous step)

of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), err = ESUCCESS, files = files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)], ino = 0, ino0 = m0 + n0, ino1 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, n0 ≠ 0, dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, n0 ≤ # buf0 ⊦ [while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(ino1, inode, buf0, ino0, dirs; ino, isdir, err, files, asynced); ino4 := ino; if ino4 ≠ 0 then err := ESUCCESS; dirs1 := dirs; if err = ESUCCESS then let ino = m1 in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, 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)), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule invariant right

And obtained the following new goals

Proof step 366:
files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, files = files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)], ino = 0, ino0 = m0 + n0, ino1 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0), fd ∈ of, m ∈ files0, n0 ≤ # buf0 ⊦ n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)
Proof step 377:
files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, err0 = ESUCCESS, files1 = files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)], ino0 = m0 + n0, ino1 = m0, ino2 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, ¬ isdir0, dom of < ino3, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, n0 ≤ # buf0 ⊦ [vfs_write_block#(ino1, inode, buf0, ino0, dirs; ino, isdir, err, files, asynced)] (of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0
Proof step 493:
files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err0 = ESUCCESS, files1 = files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)], ino0 = m0 + n0, ino1 = m0, ino2 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir0, dom of < ino3, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, n0 ≤ # buf0 ⊦ [ino4 := ino; if ino4 ≠ 0 then err := ESUCCESS; dirs1 := dirs; if err = ESUCCESS then let ino = m1 in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, 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, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err = ESUCCESS ∧ ¬ isdir

Rule argument

fma: of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files) pos: right 1

Additional information

Used formulas: of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)