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Proof step 52 from proof fsync-inode-keep-abs (previous step)

dirs[m0] = mkdir(m1, md0, m2, m3, entries), icache[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), icache-cons(icache, dirs, files), m ∈ icache, m0 ∈ dirs, m ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[m] = mkfile(files[m].size, files[m].meta, files[m].nlink, files[m].content ⊕ mkcontent(m, pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 53:
icache[m] = mkientry(true, mkinode(m0, md, true, m2, m3, m1)), dirs[m0] = mkdir(m1, md0, m2, m3, entries), files[m] = mkfile(m4, md1, m5, content), icache-cons(icache, dirs, files), m ∈ files, m0 ∈ dirs, m ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[m] = mkfile(m4, md1, m5, content ⊕ mkcontent(m, 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[m], 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[m], m4, md1, m5, content