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Proof step 144 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, n ∈ content ↔ n ∈ content1, content[n] = content1[n], pcache[key] = mkpentry(boolvar, buf0), 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), 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), datakey(m, n) ∈ pcache1, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, n ∈ content1 ⊕ mkcontent(m, pcache1), ∀ 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] ) ⊦ buf = pcache1[datakey(m, n)].page, key = datakey(m, n)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 145:
# buf = VFS_PAGE_SIZE, n ∈ content ↔ n ∈ content1, 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), pcache[key] = mkpentry(boolvar, buf0), content[n] = content1[n], pcache1[datakey(m, n)] = mkpentry(boolvar1, buf2), 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), n ∈ content1 ⊕ mkcontent(m, pcache1), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, datakey(m, n) ∈ pcache1, ∀ 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) ⊦ buf = buf2, key = datakey(m, n)

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache1[datakey(m, n)], boolvar1, buf2]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache1[datakey(m, n)], boolvar1, buf2