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Proof step 69 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), cache_pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), dirs = cache_dirs, files = cache_files[m, mkfile(m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto 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), datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m ∈ cache_files, m2 ≤ n, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, cache_dirs), 0, n); dirs, files); inode1 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?; asynced1 := true; buf-opt1 := some(fill(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)); 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-opt1.buf, asynced0; err, cache_pcache)}; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt1 := 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 = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt1 = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_pcache[datakey(m, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), 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, files = cache_files[m, mkfile(m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] 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, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m2 ≤ n, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, cache_dirs), 0, n); dirs, files); inode1 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?; asynced1 := true; buf-opt1 := some(fill(some(buf0).buf, zero, m2 % VFS_PAGE_SIZE, n0)); 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-opt1.buf, asynced0; err, cache_pcache)}; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt1 := 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 = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt1 = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)