[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 825 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, asynced0 ↔ m2 ≤ m6 ∧ old_ino ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?), 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, buf-opt = buf-opt0, content = content0, ino = m3, old_ino = m2 % VFS_PAGE_SIZE, size = min(m6, m2), buf-opt0.some?, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache0), m2 ≤ m6 → old_ino ≠ 0 → VFS_PAGE_SIZE ≠ 0, ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨if asynced0 then {pageno := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := afs_files[ino].content[pageno]; buf := fill(buf, zero, old_ino, VFS_PAGE_SIZE - old_ino); content[pageno] := buf; buf-opt := some(buf)}; afs_files[ino].content := content upto size; let new_inode = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2) in {new_inode.size := m6; cache_dirs0 := cache_dirs; afs_inode_sync#(new_inode; cache_dirs, afs_files)}; 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_files[m3].meta, false, afs_files[m3].nlink, 0, afs_files[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (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 ↔ asynced1) ∧ buf-opt0 = buf-opt ∧ mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), VFS_PAGE_SIZE = 0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

Additional information