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Proof step 168 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, files1[m4] = mkfile(m6, md1, # links(m4, dirs), content2), pcache[datakey(m4, m5)] = mkpentry(false, content2[m5]), 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), m4 = m, mkfile(m0, md, # links(m, dirs), content[n, buf]) = mkfile(m1, md0, m3, content0), 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), m5 ∈ content2, datakey(m4, m5) ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, m4 ∈ files1, ⌊err0⌋ , ∀ 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] ), ∀ 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]) ⊦ m5 ∈ content0 ∧ content2[m5] = content0[m5]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 169:
# 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]

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)