[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 983 from proof refine-truncate-buff-none-uncached (previous step)

asynced0 ↔ m2 ≤ m6 ∧ old_ino ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content, cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, asynced0, buf-opt = none, cache_dirs0 = cache_dirs, content = content0, ino = m3, new_inode = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2), old_ino = m2 % VFS_PAGE_SIZE, pageno = m2 / VFS_PAGE_SIZE, size = min(m6, m2), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, pageno ∈ afs_files[ino].content, old_ino + (VFS_PAGE_SIZE - old_ino) ≤ # afs_files[ino].content[pageno], VFS_PAGE_SIZE ≥ old_ino, m2 ≤ m6 → old_ino ≠ 0 → VFS_PAGE_SIZE ≠ 0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_files0 := afs_files [ino, afs_files[ino].content:= (content[pageno, fill(afs_files[ino].content[pageno], zero, old_ino, VFS_PAGE_SIZE - old_ino)] upto size) ]; afs_inode_sync#(new_inode.size:= m6; cache_dirs, afs_files0); inode := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, afs_files0[m3].meta, false, afs_files0[m3].nlink, 0, afs_files0[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files0 = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs0), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6))] ∧ ¬ asynced ∧ none = some(fill(afs_files[ino].content[pageno], zero, old_ino, VFS_PAGE_SIZE - old_ino)) ∧ mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 984:
asynced0 ↔ m2 ≤ m6 ∧ old_ino ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, afs_files0 = afs_files[ino, afs_files[ino].content:= (content[pageno, fill(afs_files[ino].content[pageno], zero, old_ino, VFS_PAGE_SIZE - old_ino)] upto size)], asynced0, buf-opt = none, cache_dirs0 = cache_dirs, content = content0, ino = m3, new_inode = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2), old_ino = m2 % VFS_PAGE_SIZE, pageno = m2 / VFS_PAGE_SIZE, size = min(m6, m2), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, pageno ∈ afs_files[ino].content, old_ino + (VFS_PAGE_SIZE - old_ino) ≤ # afs_files[ino].content[pageno], VFS_PAGE_SIZE ≥ old_ino, cache_sync → synced(cache_files, cache_icache, cache_pcache0), m2 ≤ m6 → old_ino ≠ 0 → VFS_PAGE_SIZE ≠ 0, ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_inode_sync#(new_inode.size:= m6; cache_dirs, afs_files0); inode := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, afs_files0[m3].meta, false, afs_files0[m3].nlink, 0, afs_files0[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files0 = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs0), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6))] ∧ ¬ asynced ∧ none = some(fill(afs_files[ino].content[pageno], zero, old_ino, VFS_PAGE_SIZE - old_ino)) ∧ mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic