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Proof step 1 from proof fsync-pages-err (conclusion)

err = ESUCCESS ∨ ⌊err⌋ ⊦ [cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)] (err = ESUCCESS ∨ ⌊err⌋ )

User applied rule call right

And obtained the following new goals

Proof step 2:
asynced1 ↔ asynced, err = ESUCCESS ∨ ⌊err⌋ ⊦ [err := ESUCCESS; let n = 0, ino = inode.ino, asynced0 = ?, asynced = ? in while n * VFS_PAGE_SIZE < inode.size ∧ err = ESUCCESS do {/* (fsync-pages-overwrite : invariant afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(ino, dirs, files) = getinode(ino, dirs, files`) ∧ ino = inode.ino ∧ ino ∈ files ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache`) ∧ pcache[key].page = (pcache`)[key].page ∧ (pcache[key].dirty → (pcache`)[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[ino].content ↔ pageno ∈ (files` ⊕ pcache`)[ino].content) ∧ files[ino].content[pageno] = (files` ⊕ pcache`)[ino].content[pageno] ; (pageno ∈ files[ino].content ↔ pageno ∈ (files`)[ino].content) ∧ files[ino].content[pageno] = (files`)[ino].content[pageno] )))) */; pcache_check_page#(ino, n, pcache; asynced0, asynced, err); if asynced0 ∧ asynced then let buf = ? in {pcache_get#(ino, n, pcache; asynced0, buf, err); if err = ESUCCESS then afs_writepage#(inode, n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); if err = ESUCCESS then {asynced := false; pcache_set_status#(ino, n, asynced; err, pcache)}}; n := n + 1}] (err = ESUCCESS ∨ ⌊err⌋ )

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_fsync-pages#(INODE, DIRS; ERR, FILES, PCACHE, ASYNCED) {ERR := ESUCCESS; let N = 0, INO = INODE.ino, HIT = ?, DIRTY = ? in while N * VFS_PAGE_SIZE < INODE.size ∧ ERR = ESUCCESS do {/* (fsync-pages-overwrite : invariant afs-cons(DIRS, FILES) ∧ pcache-cons(PCACHE, DIRS, FILES) ∧ getinode(INO, DIRS, FILES) = getinode(INO, DIRS, FILES`) ∧ INO = INODE.ino ∧ INO ∈ FILES ∧ (∀ KEY. (KEY ∈ PCACHE ↔ KEY ∈ PCACHE`) ∧ PCACHE[KEY].page = (PCACHE`)[KEY].page ∧ ( PCACHE[KEY].dirty → (PCACHE`)[KEY].dirty)) ∧ ( ERR = ESUCCESS → (∀ PAGENO. (PAGENO < N ⊃ ( PAGENO ∈ FILES[INO].content ↔ PAGENO ∈ (FILES` ⊕ PCACHE`)[INO] .content) ∧ FILES[INO].content[PAGENO] = (FILES` ⊕ PCACHE`)[INO].content [PAGENO ] ; ( PAGENO ∈ FILES[INO].content ↔ PAGENO ∈ (FILES`)[INO].content) ∧ FILES[INO].content[PAGENO] = (FILES`)[INO].content[PAGENO] )))) */; pcache_check_page#(INO, N, PCACHE; HIT, DIRTY, ERR); if HIT ∧ DIRTY then let PBUF = ? in {pcache_get#(INO, N, PCACHE; HIT, PBUF, ERR); if ERR = ESUCCESS then afs_writepage# (INODE, N, PBUF, DIRS; ERR, FILES; ASYNCED); if ERR = ESUCCESS then afs_check_commit#(DIRS, FILES; ERR; ASYNCED); if ERR = ESUCCESS then {DIRTY := false; pcache_set_status#(INO, N, DIRTY; ERR, PCACHE)}}; N := N + 1} };