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Proof step 48 from proof fsync-pages-overwrite (previous step)

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), 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] ), ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]) ⊦ # buf = VFS_PAGE_SIZE

User applied rule all left

And closed the goal!

Rule argument

pos: left 13 terms: datakey(m, n) abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s) Used terms: datakey(m, n)