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Proof step 111 from proof overwrite-write-page-dirty (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 112:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), icache[ino0] = mkientry(boolvar, mkinode(m2, md0, false, m3, m4, m5)), files[ino0] = mkfile(m6, md1, m7, content0), ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ ino0 = ino, mkfile(m5, md0, m3, content0 ⊕ mkcontent(ino0, pcache)) = mkfile(m5, md0, m3, content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, 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], m6, md1, m7, content0]

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], m6, md1, m7, content0