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Proof step 107 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m0, md, # links(m, dirs), content1), pcache[datakey(m, n)] = mkpentry(true, buf), pcache1[key] = mkpentry(boolvar0, buf1), pcache[datakey(m, m6)] = mkpentry(false, content[m6]), files1[m] = mkfile(m0, md, # links(m, dirs), content), pcache[key] = mkpentry(boolvar, buf0), n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])]), pcache-cons(pcache1, dirs, files0), m6 ∈ content, datakey(m, m6) ∈ pcache, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, m6 ∈ content[n, buf], ∀ key1. key1 ∈ pcache → key1.data? ∧ # pcache[key1].page = VFS_PAGE_SIZE ∧ key1.ino ∈ files1 ∧ (¬ pcache[key1].dirty → key1.part ∈ files1[key1.ino].content ∧ pcache[key1].page = files1[key1.ino].content[key1.part]), ∀ pageno. (pageno < n ⊃ (pageno ∈ content ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content ↔ pageno ∈ content1) ∧ content[pageno] = content1[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ content[m6] = content[n, buf][m6], datakey(m, m6) = datakey(m, n), key = datakey(m, n)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: file-content name: At-other seq: ⊦ n ≠ n0 → content[n0, buf][n] = content[n] subst: [n, buf, n0, content] → [m6, buf, n, content] flags: <all paths>

Additional information

Used terms: m6, buf, n, content