[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 248 from proof inv-truncate-buff-none-uncached (previous step)

asynced0 ↔ inode.size ≤ n ∧ old_ino ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), ¬ asynced0, buf-opt = none, content = files0[inode.ino].content, err = ESUCCESS, files = files0[ino, files0[ino].content:= (content upto size)], ino = inode.ino, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), new_inode = inode, old_ino = inode.size % VFS_PAGE_SIZE, old_ino0 = 0, pageno = m2 / VFS_PAGE_SIZE, size = min(n, inode.size), size0 = 0, afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m ∈ files0, asynced2 → synced(files0, icache, pcache) ⊦ [afs_inode_sync#(new_inode.size:= n; dirs, files); inode := getinode(inode.ino, dirs, files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪asynced4 := asynced0; if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), VFS_PAGE_SIZE = 0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 249:
files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0[m, mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2))], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m ∈ files0, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced2 → synced(files0, icache, pcache) ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files); 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, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪asynced4 := false; if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, none.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), m2 ≤ n ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2).size:= m6 = mkinode(m, md, boolvar, m0, m1, m6); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ ¬ none.some?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)