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Proof step 156 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, 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), 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), key ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, ⌊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] ) ⊦ key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[n, buf]);files1[key.ino]).content ∧ pcache[key].page = (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[n, buf]);files1[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 157:
# buf = VFS_PAGE_SIZE, 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), pcache[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(pcache, dirs, files1), pcache-cons(pcache1, dirs, files0), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, key ∈ pcache, ⌊err0⌋ , ∀ 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.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ ( ¬ boolvar → key.part ∈ (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[n, buf]);files1[key.ino]).content ∧ buf0 = (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[n, buf]);files1[key.ino]).content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[key], boolvar, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key], boolvar, buf0