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Proof step 7 from proof refine-truncate-buff-none-uncached (previous step)

asynced ↔ asynced0, afs_asynced ↔ cache_asynced, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = none, err = err0, inode = mkinode(m, md, false, m1, 0, 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), m ∈ cache_files, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced, err, cache_dirs, cache_files, cache_asynced, cache_icache, cache_pcache)⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced0, 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 ↔ asynced0) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 8:
asynced4 ↔ asynced, asynced3 ↔ cache_asynced, afs_asynced ↔ cache_asynced, asynced ↔ asynced0, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = none, dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, inode = mkinode(m, md, false, m1, 0, m2), pageno = m2 / VFS_PAGE_SIZE, pcache = cache_pcache, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪if pre-truncate(inode, n, pageno, buf-opt, dirs, files) then let ino = inode.ino, size = inode.size, asynced2 = buf-opt.some?, asynced1 = false, asynced0 = false in {err := ESUCCESS; if buf-opt.none? then let buf = ? in {pcache_check_page#(ino, pageno, pcache; asynced1, asynced0, err); if err = ESUCCESS ∧ asynced1 then pcache_get#(ino, pageno, pcache; asynced1, buf, err); if err = ESUCCESS ∧ asynced1 then buf-opt := some(buf)}; if err = ESUCCESS then afs_truncate#(n, pageno; buf-opt, inode, asynced4, err, dirs, files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, size, n; err, pcache); if asynced4 then pcache_set#(inode.ino, pageno, buf-opt.buf, asynced; err, pcache)}; if (¬ asynced4 ∨ err ≠ ESUCCESS) ∧ ¬ asynced2 then buf-opt := none} else abort⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced0, err0, afs_dirs, afs_files, afs_asynced)⟩ ( afs_dirs = dirs ∧ afs_files = (files ⊕ pcache) ⊕ icache ∧ (afs_asynced ↔ asynced3) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced4 ↔ asynced0) ∧ err = err0), VFS_PAGE_SIZE = 0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_truncate# (N, PAGENO ; PBUF-OPT, INODE, MODIFIED, ERR, DIRS, FILES, ASYNCED, ICACHE, PCACHE ) {if pre-truncate(INODE, N, PAGENO, PBUF-OPT, DIRS, FILES) then let INO = INODE.ino, SIZE = INODE.size, SOME_BUF = PBUF-OPT.some?, HIT = false, OLD_DIRTY = false in {ERR := ESUCCESS; if PBUF-OPT.none? then let PBUF = ? in {pcache_check_page# (INO, PAGENO, PCACHE; HIT, OLD_DIRTY, ERR); if ERR = ESUCCESS ∧ HIT then pcache_get# (INO, PAGENO, PCACHE; HIT, PBUF, ERR); if ERR = ESUCCESS ∧ HIT then PBUF-OPT := some(PBUF)}; if ERR = ESUCCESS then afs_truncate# (N, PAGENO ; PBUF-OPT, INODE, MODIFIED, ERR, DIRS, FILES, ASYNCED); if ERR = ESUCCESS then let DIRTY = false in {icache_set#(INODE, DIRTY; ERR, ICACHE); pcache_truncate#(INODE.ino, SIZE, N; ERR, PCACHE); if MODIFIED then pcache_set# (INODE.ino, PAGENO, PBUF-OPT.buf, DIRTY ; ERR, PCACHE)}; if (¬ MODIFIED ∨ ERR ≠ ESUCCESS) ∧ ¬ SOME_BUF then PBUF-OPT := none} else abort };% ⊦ VFS_PAGE_SIZE ≠ 0; (s)