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

asynced ↔ asynced5, afs_asynced ↔ cache_asynced, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = none, err = ESUCCESS, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), m1 = # links(m, cache_dirs), 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), m ∈ cache_files, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced, err, cache_dirs, cache_files, cache_asynced); 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 asynced then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced0; err, cache_pcache)}; if ¬ asynced ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced ↔ asynced5) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 39:
asynced0 ↔ asynced1, asynced ↔ cache_asynced, afs_asynced ↔ cache_asynced, asynced1 ↔ asynced5, cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = none, dirs = cache_dirs, err = ESUCCESS, files = cache_files, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), m1 = # links(m, cache_dirs), pageno = m2 / VFS_PAGE_SIZE, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪if pre-truncate(inode, n, pageno, buf-opt, dirs, files) then let old_ino = 0, size = 0 in afs_truncate_internal#(n, pageno; inode, buf-opt, old_ino, size, asynced0, err, dirs, files; asynced) else abort; asynced1 := asynced0; 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, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, afs_dirs, afs_files, afs_asynced)⟩ ( afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), VFS_PAGE_SIZE = 0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_truncate# (N, PAGENO; PBUF-OPT, INODE, MODIFIED, ERR, DIRS, FILES, ASYNCED) {if pre-truncate(INODE, N, PAGENO, PBUF-OPT, DIRS, FILES) then let OFFSET = 0, SIZE = 0 in afs_truncate_internal# (N, PAGENO ; INODE, PBUF-OPT, OFFSET, SIZE, MODIFIED, ERR, DIRS, FILES ; ASYNCED) else abort };% ⊦ VFS_PAGE_SIZE ≠ 0; (s)