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Proof step 111 from proof refine-iget (previous step)

afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, ino0 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ( (cache_files ⊕ cache_pcache) ⊕ cache_icache[ino, mkientry(false, mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].size))] )[ino0 ], ino ∈ cache_icache, ino ∈ cache_dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 112:
cache_files[ino] = mkfile(m, md, m0, content), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino0 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[ino, mkientry(false, mkinode(ino, md, false, m0, 0, m))])[ino0], ino ∈ cache_dirs, ino ∈ cache_icache

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] → [cache_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: cache_files[ino], m, md, m0, content