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Proof step 84 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n), mkpentry(false, buf)][key] = mkpentry(boolvar, buf0), files1[m] = mkfile(m0, md, # links(m, dirs), content), files0[m] = mkfile(m0, md, # links(m, dirs), content1), pcache[datakey(m, n)] = mkpentry(true, buf), pcache1[key] = mkpentry(boolvar0, buf1), 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(pcache, dirs, files1), pcache-cons(pcache1, dirs, files0), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ∀ 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) ⊦ ∀ key. key ∈ pcache[datakey(m, n), mkpentry(false, buf)] → key.data? ∧ # pcache[datakey(m, n), mkpentry(false, buf)][key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])]) ∧ ( ¬ pcache[datakey(m, n), mkpentry(false, buf)][key].dirty → key.part ∈ files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])][key.ino].content ∧ pcache[datakey(m, n), mkpentry(false, buf)][key].page = files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])][key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 85:
# buf = VFS_PAGE_SIZE, 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), 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), pcache-cons(pcache, dirs, files1), key0 ∈ pcache[datakey(m, n), mkpentry(false, buf)], m ∈ files0, m ∈ files1, 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 ∈ content ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content ↔ pageno ∈ content1) ∧ content[pageno] = content1[pageno] ) ⊦ key0.data? ∧ # pcache[datakey(m, n), mkpentry(false, buf)][key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ ( ¬ pcache[datakey(m, n), mkpentry(false, buf)][key0].dirty → key0.part ∈ (key0.ino = m ⊃ mkfile(m0, md, # links(key0.ino, dirs), content[n, buf]);files1[key0.ino]).content ∧ pcache[datakey(m, n), mkpentry(false, buf)][key0].page = (key0.ino = m ⊃ mkfile(m0, md, # links(key0.ino, dirs), content[n, buf]);files1[key0.ino]).content[key0.part])

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)