[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 179 from proof write-term (previous step)

of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs), content0), buf1 = buf0, dirs1 = dirs, err = ESUCCESS, files = files0[m, mkfile(m2, md0, # links(m, dirs), content0 upto m2)], ino3 = 0, inode1 = mkinode(m, md0, false, # links(m, dirs), 0, m2), n2 = m0, n3 = m0 + n0, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(m2, md0, # links(m, dirs), content0 upto m2)]), afs-cons(dirs, files), of-cons(of, dirs, files0), valid-file-inode(mkinode(m, md0, false, # links(m, dirs), 0, m2), dirs, files), m ∈ files0, fd ∈ of, n0 ≤ # buf0, m0 + ino3 ≤ m0 + n0, m0 + n0 - m0 ≤ # buf0 ⊦ [vfs_write_loop#(m0, mkinode(m, md0, false, # links(m, dirs), 0, m2), m0 + n0, buf0, dirs; ino3, err, files, asynced)] ( valid-file-inode(inode1, dirs1, files) → ⟪if ino3 ≠ 0 then err := ESUCCESS; dirs0 := dirs; if err = ESUCCESS then let ino = m2 in {n0 := ino3, ino1 := m0 + ino3; if ino3 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md0, 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}⟫ (dirs0 = dirs)), n0 = 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 180:
files0[m] = mkfile(m2, md0, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, files = files0[m, mkfile(m2, md0, # links(m, dirs), content0 upto m2)], ino3 = 0, n0 ≠ 0, afs-cons(dirs, files0[m, mkfile(m2, md0, # links(m, dirs), content0 upto m2)]), afs-cons(dirs, files0), of-cons(of, dirs, files0), fd ∈ of, m ∈ files0, n0 ≤ # buf0 ⊦ [vfs_write_loop#(m0, mkinode(m, md0, false, # links(m, dirs), 0, m2), m0 + n0, buf0, dirs; ino3, err, files, asynced)] ( m ∈ files ∧ # links(m, dirs) = files[m].nlink → ⟪if ino3 ≠ 0 then err := ESUCCESS; dirs0 := dirs; if err = ESUCCESS then let ino = m2 in {n0 := ino3, ino1 := m0 + ino3; if ino3 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md0, 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}⟫ (dirs0 = dirs)), mode ≠ MODE_W ∧ mode ≠ MODE_RW, m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ m ≤ m + n; (s)% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n - m = n; (s)