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Proof step 626 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), icache[m] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), files0[m] = mkfile(m0, md, m1, content), files1[m] = mkfile(m9, md2, m10, content1), content[n0] = pcache0[datakey(m, n0)].page, n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n0) ∈ pcache0, m ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, m ∈ icache, n0 ∈ content, n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache), ⌊err0⌋ ⊦ content[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0], datakey(m, n0) ∈ pcache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 627:
# buf = VFS_PAGE_SIZE, content[n0] = buf0, files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m0, md, m1, content), icache[m] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), pcache0[datakey(m, n0)] = mkpentry(boolvar0, buf0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache), n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content, m ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, m ∈ files1, datakey(m, n0) ∈ pcache0, ⌊err0⌋ ⊦ content[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0], datakey(m, n0) ∈ pcache

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache0[datakey(m, n0)], boolvar0, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache0[datakey(m, n0)], boolvar0, buf0