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Proof step 96 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, (key0.ino = m ⊃ mkfile(m0, md, # links(key0.ino, dirs), content[n, buf]);mkfile(m4, md1, # links(key0.ino, dirs), content2)) = mkfile(m1, md0, m3, content0), 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), pcache[key0] = mkpentry(false, content2[key0.part]), files1[key0.ino] = mkfile(m4, md1, # links(key0.ino, dirs), content2), key0.data?, 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), key0.part ∈ content2, key0.ino ∈ files1, key0 ∈ pcache, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ∀ key1. key1 ∈ pcache → key1.data? ∧ # pcache[key1].page = VFS_PAGE_SIZE ∧ key1.ino ∈ files1 ∧ (¬ pcache[key1].dirty → key1.part ∈ files1[key1.ino].content ∧ pcache[key1].page = files1[key1.ino].content[key1.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) ⊦ key0 = datakey(m, n), key0.part ∈ content0 ∧ content2[key0.part] = content0[key0.part]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 97:
# buf = VFS_PAGE_SIZE, (m5 = m ⊃ mkfile(m0, md, # links(m5, dirs), content[n, buf]);mkfile(m4, md1, # links(m5, dirs), content2)) = mkfile(m1, md0, m3, content0), files1[m5] = mkfile(m4, md1, # links(m5, dirs), content2), pcache[key0] = mkpentry(false, content2[m6]), 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), key0 = datakey(m5, m6), key0.data?, 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), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, key0 ∈ pcache, m5 ∈ files1, m6 ∈ content2, ∀ 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] ), ∀ key1. key1 ∈ pcache → key1.data? ∧ # pcache[key1].page = VFS_PAGE_SIZE ∧ key1.ino ∈ files1 ∧ (¬ pcache[key1].dirty → key1.part ∈ files1[key1.ino].content ∧ pcache[key1].page = files1[key1.ino].content[key1.part]) ⊦ key0 = datakey(m, n), m6 ∈ content0 ∧ content2[m6] = content0[m6]

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key0, m5, m6]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key0, m5, m6