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Proof step 7 from proof overwrite-write-inode-clean-file (previous step)

icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), ino ∈ files, ino ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m, md, m1, files[ino].content ⊕ mkcontent(ino, pcache))] = (files[ino, (files[ino].meta:= md).size:= m] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), files[ino] = mkfile(m4, md1, m5, content), ino ∈ icache, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m, md, m1, content ⊕ mkcontent(ino, pcache))] = (files[ino, (files[ino].meta:= md).size:= m] ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m0, md, false, m1, m2, m))]

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[ino], m4, md1, m5, 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[ino], m4, md1, m5, content