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Proof step 63 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, asynced2 ↔ asynced5, asynced0 ↔ inode.size ≤ n ∧ old_ino ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?), 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), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, asynced0, buf-opt = some(buf0), content = files[inode.ino].content, dirs = cache_dirs, err = ESUCCESS, files = cache_files, ino = inode.ino, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), old_ino = inode.size % VFS_PAGE_SIZE, old_ino0 = 0, pageno = m2 / VFS_PAGE_SIZE, size = min(n, inode.size), size0 = 0, buf-opt.some?, 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, old_ino + (VFS_PAGE_SIZE - old_ino) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ old_ino, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪files[ino].content := content[pageno, fill(buf-opt.buf, zero, old_ino, VFS_PAGE_SIZE - old_ino)] upto size; let new_inode = inode in {new_inode.size := n; afs_inode_sync#(new_inode; dirs, files)}; inode := getinode(inode.ino, dirs, files); err := ESUCCESS; asynced := ?; asynced1 := asynced0; buf-opt1 := some(fill(buf-opt.buf, 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-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 ∧ inode = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), VFS_PAGE_SIZE = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 64:
# buf0 = VFS_PAGE_SIZE, asynced0 ↔ inode.size ≤ n ∧ old_ino ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?), asynced2 ↔ asynced5, ((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), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, asynced0, buf-opt = some(buf0), content = files[inode.ino].content, dirs = cache_dirs, err = ESUCCESS, files = cache_files, ino = inode.ino, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), old_ino = inode.size % VFS_PAGE_SIZE, old_ino0 = 0, pageno = m2 / VFS_PAGE_SIZE, size = min(n, inode.size), size0 = 0, buf-opt.some?, 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, old_ino + (VFS_PAGE_SIZE - old_ino) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ old_ino, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪let new_inode = inode in {new_inode.size := n; files[ino].content := content[pageno, fill(buf-opt.buf, zero, old_ino, VFS_PAGE_SIZE - old_ino)] upto size; afs_inode_sync#(new_inode; dirs, files)}; inode := getinode(inode.ino, dirs, files); err := ESUCCESS; asynced := ?; asynced1 := asynced0; buf-opt1 := some(fill(buf-opt.buf, 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-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 ∧ inode = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), VFS_PAGE_SIZE = 0

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ some(buf).some?; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ some(buf).buf = buf; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic