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Proof step 360 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);mkfile(m7, md1, m8, content0)) = mkfile(m11, md3, m12, content2), pcache0[datakey(ino, n0)] = mkpentry(boolvar0, pcache[datakey(ino, n0)].page), files1[ino] = mkfile(m9, md2, m10, content1), files0[ino] = mkfile(m7, md1, m8, content0), icache[ino] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(ino, n0) ∈ pcache, n0 ∈ content1 ⊕ mkcontent(ino, pcache0), n0 ∈ content0 ⊕ mkcontent(ino, pcache), ino ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, datakey(ino, n0) ∈ pcache0, n0 ∈ content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]), ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(ino, pcache0))[n0] = (content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]))[n0]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 361:
# buf = VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);mkfile(m7, md1, m8, content0)) = mkfile(m11, md3, m12, content2), files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), files0[ino] = mkfile(m7, md1, m8, content0), files1[ino] = mkfile(m9, md2, m10, content1), pcache0[datakey(ino, n0)] = mkpentry(boolvar0, buf0), pcache[datakey(ino, n0)] = mkpentry(boolvar1, buf0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]), datakey(ino, n0) ∈ pcache0, ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, n0 ∈ content0 ⊕ mkcontent(ino, pcache), n0 ∈ content1 ⊕ mkcontent(ino, pcache0), datakey(ino, n0) ∈ pcache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(ino, pcache0))[n0] = (content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]))[n0]

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(ino, n0)], boolvar1, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(ino, n0)], boolvar1, buf0