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Proof step 28 from proof overwrite-write-inode-clean-file (previous step)

icache[ino0] = mkientry(boolvar0, mkinode(m6, md2, false, m7, m8, m9)), icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), files[ino] = mkfile(m4, md1, m5, content), ino ∈ icache, ino ∈ files, ino0 ∈ files, ino0 ∈ icache ⊦ ino0 = ino, mkfile(m9, md2, m7, files[ino0].content ⊕ mkcontent(ino0, pcache)) = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
files[ino] = mkfile(m4, md1, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), icache[ino0] = mkientry(boolvar0, mkinode(m6, md2, false, m7, m8, m9)), files[ino0] = mkfile(m10, md3, m11, content0), ino0 ∈ icache, ino0 ∈ files, ino ∈ files, ino ∈ icache ⊦ ino0 = ino, mkfile(m9, md2, m7, content0 ⊕ mkcontent(ino0, pcache)) = ((files[ino, mkfile(m, md, m5, content)] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))])[ino0]

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], m10, md3, m11, 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], m10, md3, m11, content0