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Proof step 169 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), pcache[datakey(m, m5)] = mkpentry(false, content[m5]), files1[m] = mkfile(m0, md, # links(m, dirs), content), 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), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, datakey(m, m5) ∈ pcache, m5 ∈ content, m5 ∈ content[n, buf], ⌊err0⌋ , ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.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[m5] = content[n, buf][m5]

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] → [m5, buf, n, content] flags: <all paths>

Additional information

Used simplifier rules: ⊦ content[n, buf][n] = buf; (s)% ⊦ n ∈ content[n, buf]; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws) Used terms: m5, buf, n, content