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Proof step 298 from proof overwrite-write-page-clean (previous step)

icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ ino0 = ino, mkfile(m7, md1, m5, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(m7, md1, m5, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 299:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ ino0 = ino, mkfile(m7, md1, m5, content1 ⊕ mkcontent(ino0, pcache)) = mkfile(m7, md1, m5, content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[ino0], m8, md2, m9, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[ino0], m8, md2, m9, content1