Proof step 703 from proof refine-truncate-buff-some (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

• Proof step 704:

  # buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, ((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 )[m3, mkfile(m0, md0, # links(m3, cache_dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], cache_dirs2 = cache_dirs, dirs = cache_dirs, files = afs_files, ino = inode.ino, inode = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m), buf-opt0.some?, 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), ino ∈ dirs, m3 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨dirs[ino].meta := inode.meta; inode := (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, files[m3].meta, false, files[m3].nlink, 0, files[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs2 ∧ files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m))] ∧ (asynced ↔ asynced1) ∧ (m3 ∈ cache_dirs2 ⊃ mkinode(m3, cache_dirs2[m3].meta, true, cache_dirs2[m3].nlink, cache_dirs2[m3].nsubdirs, cache_dirs2[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ ( (cache_files ⊕ cache_pcache0) ⊕ cache_icache = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] ∧ (asynced ↔ asynced1) ∧ some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) = buf-opt0 ∧ mkinode(m3, md, false, # links(m3, cache_dirs), 0, m) = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2) ∧ asynced2 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, ino ∈ files

• Proof step 708:

  # buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, ((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 )[m3, mkfile(m0, md0, # links(m3, cache_dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], cache_dirs2 = cache_dirs, dirs = cache_dirs, files = afs_files, ino = inode.ino, inode = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m), buf-opt0.some?, 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, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨skip; inode := (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, files[m3].meta, false, files[m3].nlink, 0, files[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs2 ∧ files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m))] ∧ (asynced ↔ asynced1) ∧ (m3 ∈ cache_dirs2 ⊃ mkinode(m3, cache_dirs2[m3].meta, true, cache_dirs2[m3].nlink, cache_dirs2[m3].nsubdirs, cache_dirs2[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ ( (cache_files ⊕ cache_pcache0) ⊕ cache_icache = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] ∧ (asynced ↔ asynced1) ∧ some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) = buf-opt0 ∧ mkinode(m3, md, false, # links(m3, cache_dirs), 0, m) = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2) ∧ asynced2 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, ino ∈ files, ino ∈ dirs

Rule argument

Additional information