[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 22 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), buf-opt.some?, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced → synced(files, icache, pcache) ⊦ [afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, dirs, files, asynced3)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; skip⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))))

User applied rule call right

And obtained the following new goals

Proof step 23:
# buf-opt.buf = VFS_PAGE_SIZE, asynced0 ↔ asynced4, asynced ↔ asynced3, files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), pageno = m2 / VFS_PAGE_SIZE, buf-opt.some?, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, 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] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced0 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; skip⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), VFS_PAGE_SIZE = 0

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 };