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Proof step 59 from proof refine-truncate-buff-none-uncached (previous step)

asynced2 ↔ asynced5, asynced0 ↔ inode.size ≤ n ∧ old_ino ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, asynced0, buf-opt = none, content = files[inode.ino].content, dirs = cache_dirs, err = ESUCCESS, files = cache_files, files0 = files[ino, files[ino].content:= (content[pageno, fill(files[ino].content[pageno], zero, old_ino, VFS_PAGE_SIZE - old_ino)] upto size)], ino = inode.ino, inode = mkinode(m, md, false, # links(m, cache_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(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, pageno ∈ files[ino].content, old_ino + (VFS_PAGE_SIZE - old_ino) ≤ # files[ino].content[pageno], VFS_PAGE_SIZE ≥ old_ino, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_inode_sync#(new_inode.size:= n; dirs, files0); inode := getinode(inode.ino, dirs, files0); err := ESUCCESS; asynced := ?; asynced1 := asynced0; buf-opt := some(fill(files[ino].content[pageno], zero, old_ino, VFS_PAGE_SIZE - old_ino)); if err = ESUCCESS then let asynced0 = false in {icache_set#(inode, asynced0; err, cache_icache); pcache_truncate#(inode.ino, m2, n; err, cache_pcache); if asynced1 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced0; err, cache_pcache)}; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, # links(m, cache_dirs), 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (files0 ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), VFS_PAGE_SIZE = 0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 60:
cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), dirs = cache_dirs, files0 = cache_files [m, mkfile (m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], m2 % VFS_PAGE_SIZE ≠ 0, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ n, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, cache_dirs), 0, n); dirs, files0); inode1 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ); err := ESUCCESS; asynced := ?; asynced1 := true; buf-opt := some(fill(cache_files[m].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced0 = false in {icache_set#(inode1, asynced0; err, cache_icache); pcache_truncate#(inode1.ino, m2, n; err, cache_pcache); if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced0; err, cache_pcache)}; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, # links(m, cache_dirs), 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (files0 ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%⊦ 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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)% ⊦ ¬ none.some?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)