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Proof step 44 from proof fsync-pages-overwrite (previous step)

files[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[m] = mkfile(m1, md1, # links(m, dirs), content1), pcache[datakey(m, n)] = mkpentry(true, buf), 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), datakey(m, n) ∈ pcache, m ∈ files, m ∈ files0, ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content1) ∧ content0[pageno] = content1[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ afs-cons(dirs, files) ∧ pre-writepage(mkinode(m, md, false, # links(m, dirs), 0, m2), n, buf, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m1, md1, # links(m, dirs), content1), files[m] = mkfile(m1, md1, # links(m, dirs), content0), n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files0, m ∈ files, datakey(m, n) ∈ pcache, ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty), ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content1) ∧ content0[pageno] = content1[pageno] ) ⊦ # buf = VFS_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-writepage(inode, n, buf, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ # buf = VFS_PAGE_SIZE; (s)