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Proof step 161 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), pcache[datakey(m, n0)] = mkpentry(boolvar1, content1[n0]), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), n0 ∈ content ⊕ mkcontent(m, pcache), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, datakey(m, n0) ∈ pcache, n0 ∈ content1, 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]) ⊦ content1[n0] = pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)].page, m ∈ icache, datakey(m, n0) ∈ pcache0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 162:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n0)] = mkpentry(boolvar1, content1[n0]), files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m9, md2, m10, content), pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)] = mkpentry(boolvar2, buf0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], n0 ∈ content1, datakey(m, n0) ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, n0 ∈ content ⊕ mkcontent(m, pcache), n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ content1[n0] = buf0, datakey(m, n0) ∈ pcache0, m ∈ icache

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, buf0]

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, buf0