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Proof step 28 from proof fsync-pages-overwrite (previous step)

pcache[datakey(m, n)] = mkpentry(true, buf0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), files[m] = mkfile(m0, md0, # links(m, dirs), content0), asynced0, err = ESUCCESS, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), datakey(m, n) ∈ pcache, m ∈ files0, m ∈ files, ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty), ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content) ∧ content0[pageno] = content[pageno] ) ⊦ [pcache_get#(m, n, pcache; asynced0, buf, err); inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if err = ESUCCESS then afs_writepage#(inode, n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); ino := m; if err = ESUCCESS then {asynced := false; pcache_set_status#(ino, n, asynced; err, pcache)}; n := n + 1] ( afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) = mkinode(inode.ino, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ∧ ino = inode.ino ∧ inode.ino ∈ files ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[inode.ino].content ↔ pageno ∈ files0[inode.ino].content ⊕ mkcontent(inode.ino, pcache1)) ∧ files[inode.ino].content[pageno] = (files0[inode.ino].content ⊕ mkcontent(inode.ino, pcache1))[pageno] ; (pageno ∈ files[inode.ino].content ↔ pageno ∈ files0[inode.ino].content) ∧ files[inode.ino].content[pageno] = files0[inode.ino].content[pageno] ))))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 29:
asynced ↔ asynced0, files[m] = mkfile(m0, md0, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), pcache[datakey(m, n)] = mkpentry(true, buf0), asynced0, err = ESUCCESS, ino = m, pageno = n, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files), afs-cons(dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache1, dirs, files0), m ∈ files, m ∈ files0, datakey(m, n) ∈ pcache, ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content) ∧ content0[pageno] = content[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ [let key = datakey(ino, pageno) in if key ∈ pcache then let pe = pcache[key] in {buf := pe.page; asynced := true} else asynced := false; err := ESUCCESS; inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if err = ESUCCESS then afs_writepage#(inode, n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); ino := m; if err = ESUCCESS then {asynced := false; pcache_set_status#(ino, n, asynced; err, pcache)}; n := n + 1] ( afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) = mkinode(inode.ino, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ∧ ino = inode.ino ∧ inode.ino ∈ files ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[inode.ino].content ↔ pageno ∈ files0[inode.ino].content ⊕ mkcontent(inode.ino, pcache1)) ∧ files[inode.ino].content[pageno] = (files0[inode.ino].content ⊕ mkcontent(inode.ino, pcache1))[pageno] ; (pageno ∈ files[inode.ino].content ↔ pageno ∈ files0[inode.ino].content) ∧ files[inode.ino].content[pageno] = files0[inode.ino].content[pageno] ))))

Rule argument

pos: right 1

Additional information

Used simplifier rules: pcache_get#(INO, PAGENO, PCACHE; HIT, BUF, ERR) {let KEY = datakey(INO, PAGENO) in if KEY ∈ PCACHE then let PE = PCACHE[KEY] in {BUF := PE.page; HIT := true} else HIT := false; ERR := ESUCCESS };