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

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, ino = m1, inode1 = (m1 ∈ cache_dirs ⊃ mkinode(m1, cache_dirs[m1].meta, true, cache_dirs[m1].nlink, cache_dirs[m1].nsubdirs, cache_dirs[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs), 0, m) ), n = m, pcache = cache_pcache, size = m2, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ 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_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ pcache → key.data? ⊦ ⟪buf-opt := some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)); asynced1 := true; cache_pcache := truncate(ino, min(n, size), pcache); if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, false; err, cache_pcache); if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m1, md, false, # links(m1, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs0 := cache_dirs; afs_truncate#(m, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs2), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m))] ∧ ¬ cache_asynced ∧ buf-opt = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 90:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)), err = ESUCCESS, ino = m1, inode1 = (m1 ∈ cache_dirs ⊃ mkinode(m1, cache_dirs[m1].meta, true, cache_dirs[m1].nlink, cache_dirs[m1].nsubdirs, cache_dirs[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs), 0, m) ), n = m, pcache = cache_pcache, size = m2, 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), m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ m, m2 % VFS_PAGE_SIZE + n0 ≤ # content[m2 / VFS_PAGE_SIZE], cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ key. key ∈ pcache → key.data? ⊦ ⟪asynced1 := true; cache_pcache := truncate(ino, min(n, size), pcache); if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, false; err, cache_pcache); if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m1, md, false, # links(m1, cache_dirs), 0, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs0 := cache_dirs; afs_truncate#(m, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = cache_dirs3 ∧ afs_files = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs2), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m))] ∧ ¬ cache_asynced ∧ buf-opt = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)