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Proof step 3 from proof at-pcache-overwrite-other (previous step)

⊦ ino = key0.ino, mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache[key0, pe])) = mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
files[ino] = mkfile(m, md, m0, content) ⊦ ino = key0.ino, mkfile(m, md, m0, content ⊕ mkcontent(ino, pcache[key0, pe])) = mkfile(m, md, m0, content ⊕ mkcontent(ino, 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[ino], m, md, m0, 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], m, md, m0, content