[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 57 from proof inv-write (previous step)

VFS_PAGE_SIZE = n1 + m1 % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content0), dirs1 = dirs, files0 = files [m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m1), dom of < ino3, afs-cons(dirs, files), of-cons(of, dirs, files), m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files, fd ∈ of, n0 ≤ # buf0, m1 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, m1); dirs, files0); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ); err := ESUCCESS; asynced := ?; ino4 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n0, buf0, dirs; ino4, err, files0, asynced); if ino4 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files0; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files0; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files0) ∧ dom of < ino3 ∧ afs-cons(dirs, files0)), m1 % VFS_PAGE_SIZE = 0, n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
VFS_PAGE_SIZE = n1 + m1 % VFS_PAGE_SIZE, files[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs1 = dirs, files0 = files [m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m1), m1 % VFS_PAGE_SIZE ≠ 0, n0 ≠ 0, dom of < ino3, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, m ∈ files, m1 / VFS_PAGE_SIZE ∈ content0, n0 ≤ # buf0 ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, m1); dirs, files0); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ); err := ESUCCESS; asynced := ?; ino4 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n0, buf0, dirs; ino4, err, files0, asynced); if ino4 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files0; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files0; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files0) ∧ dom of < ino3 ∧ afs-cons(dirs, files0)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)