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Proof step 12 from proof fsync-pages-overwrite (previous step)

asynced5 ↔ asynced2, files0[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, err0 = ESUCCESS, files1 = files0, getinode(ino, dirs, files) = getinode(ino, dirs, files1), ino = inode.ino, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), n0 = 0, pcache0 = pcache1, n * VFS_PAGE_SIZE < inode.size, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files0, ino ∈ files, err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[ino].content ↔ pageno ∈ (files1 ⊕ pcache1)[ino].content) ∧ files[ino].content[pageno] = (files1 ⊕ pcache1)[ino].content[pageno] ;(pageno ∈ files[ino].content ↔ pageno ∈ files1[ino].content) ∧ files[ino].content[pageno] = files1[ino].content[pageno] )), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ [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] ( afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(ino, dirs, files) = getinode(ino, dirs, files1) ∧ ino = inode.ino ∧ 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[ino].content ↔ pageno ∈ (files1 ⊕ pcache1)[ino].content) ∧ files[ino].content[pageno] = (files1 ⊕ pcache1)[ino].content[pageno] ;(pageno ∈ files[ino].content ↔ pageno ∈ files1[ino].content) ∧ files[ino].content[pageno] = files1[ino].content[pageno] ))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
files[m].nlink = # links(m, dirs), files0[m] = mkfile(files[m].size, files[m].meta, # links(m, dirs), content), err = ESUCCESS, 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, ∀ pageno. (pageno < n ⊃ (pageno ∈ files[m].content ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ files[m].content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ files[m].content ↔ pageno ∈ content) ∧ files[m].content[pageno] = content[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ [pcache_check_page#(m, n, pcache; asynced0, asynced, err); inode := mkinode(m, md, false, # links(m, dirs), 0, m2); ino := m; 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] ( 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

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)