[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 write-term (previous step)

files[m] = mkfile(m2, md0, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs0 = dirs, files0 = files [m, mkfile (m2, md0, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, n0 ≠ 0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, m ∈ files, m2 / VFS_PAGE_SIZE ∈ content0, n0 ≤ # buf0 ⊦ [afs_inode_sync#(mkinode(m, md0, false, # links(m, dirs), 0, m2); 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 := ?] ( afs-cons(dirs, files0) → ⟪ino3 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n0, buf0, dirs; ino3, err, files0, asynced); if ino3 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n0 := ino3, ino1 := m0 + ino3; if ino3 ≠ 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}⟫ (dirs0 = dirs)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m2, md0, # links(m, dirs), content0), dirs0 = dirs, files0 = files [m, mkfile(m2, md0, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], inode = mkinode(m, md0, false, # links(m, dirs), 0, m2), afs-cons(dirs, files), of-cons(of, dirs, files), m2 / VFS_PAGE_SIZE ∈ content0, m ∈ files, fd ∈ of, n0 ≤ # buf0, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_inode_sync#(mkinode(m, md0, false, # links(m, dirs), 0, m2); 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 := ?] ( afs-cons(dirs, files0) → ⟪ino3 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n0, buf0, dirs; ino3, err, files0, asynced); if ino3 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n0 := ino3, ino1 := m0 + ino3; if ino3 ≠ 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}⟫ (dirs0 = dirs)), m2 % VFS_PAGE_SIZE = 0, n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n