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Proof step 240 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m7, md1, m8, content1), pcache[datakey(m, n0)] = mkpentry(boolvar1, buf0), pcache0[datakey(m, n0)] = mkpentry(boolvar, buf0), icache[m] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m7, md1, m8, content0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n0) ∈ pcache, n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content0 ⊕ mkcontent(m, pcache), m ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, m ∈ files1, datakey(m, n0) ∈ pcache0, n0 ∈ content0[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), datakey(m, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ buf0 = pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)].page

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 241:
# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m7, md1, m8, content0), pcache[datakey(m, n)] = mkpentry(true, buf), icache[m] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), pcache0[datakey(m, n0)] = mkpentry(boolvar, buf0), pcache[datakey(m, n0)] = mkpentry(boolvar1, buf0), files1[m] = mkfile(m7, md1, m8, content1), pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)] = mkpentry(boolvar2, buf1), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], n0 ∈ content0[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), datakey(m, n0) ∈ pcache0, m ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, m ∈ icache, n0 ∈ content0 ⊕ mkcontent(m, pcache), n0 ∈ content1 ⊕ mkcontent(m, pcache0), datakey(m, n0) ∈ pcache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ buf0 = buf1

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)], boolvar2, buf1]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)], boolvar2, buf1