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Proof step 99 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, (m5 = m ⊃ mkfile(m0, md, # links(m, dirs), content[n, buf]);mkfile(m4, md1, # links(m5, dirs), content2)) = mkfile(m1, md0, m3, content0), files1[m5] = mkfile(m4, md1, # links(m5, dirs), content2), pcache[datakey(m5, m6)] = mkpentry(false, content2[m6]), pcache1[key] = mkpentry(boolvar0, buf1), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, # links(m, dirs), content1), files1[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, n), mkpentry(false, buf)][key] = mkpentry(boolvar, buf0), m5 = m, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), pcache-cons(pcache1, dirs, files0), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, datakey(m5, m6) ∈ pcache, m5 ∈ files1, m6 ∈ content2, ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty), ∀ 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] ), ∀ 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]) ⊦ datakey(m5, m6) = datakey(m, n), m6 ∈ content0 ∧ content2[m6] = content0[m6]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 100:
# 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[datakey(m, n), mkpentry(false, buf)][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)

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content; (ws)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)