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Proof step 52 from proof refine-write_inode (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m2, m4, m5)), cache_dirs[m] = mkdir(cache_dirs[m].size, md0, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), 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), m ∈ cache_icache, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 53:
# links(m, cache_dirs) = m3, cache_dirs[m] = mkdir(m0, md0, m3, m6, entries), cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m2, m4, m5)), cache_dirs[m] = mkdir(m0, md2, m3, m6, entries0), 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), m ∈ cache_dirs, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))]

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [cache_dirs[m], m0, md2, m3, m6, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: cache_dirs[m], m0, md2, m3, m6, entries0