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Proof step 31 from proof overwrite-write-inode-clean-dir (previous step)

icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0] = mkientry(boolvar0, mkinode(m3, md1, false, m4, m5, m6)), icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))], ino0 ∈ icache, ino ∈ icache, ino ∈ dirs, ino0 ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(m6, md1, m4, files[ino0].content ⊕ mkcontent(ino0, pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
icache[ino] = mkientry(boolvar, mkinode(m, md0, true, m0, m1, m2)), icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))][ino0] = mkientry(boolvar0, mkinode(m3, md1, false, m4, m5, m6)), files[ino0] = mkfile(m7, md2, m8, content), ino0 ∈ files, ino ∈ dirs, ino ∈ icache, ino0 ∈ icache, ino0 ∈ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))] ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile(m6, md1, m4, content ⊕ mkcontent(ino0, pcache))

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], m7, md2, m8, content]

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], m7, md2, m8, content