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Proof step 18 from proof refine-fsync (previous step)

cache_icache[m] = mkientry(boolvar0, mkinode(m, md, boolvar, m3, m4, m5)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_icache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), (boolvar0 ⊃ m3 = cache_files[m].nlink ∧ m4 = 0 ∧ ¬ boolvar ;mkinode(m, md, boolvar, m3, m4, m5) = mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) ⊦ m1 = cache_files[m].nlink

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), cache_icache[m] = mkientry(boolvar0, mkinode(m, md, boolvar, m3, m4, m5)), cache_files[m] = mkfile(m2, md1, m6, content0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), (boolvar0 ⊃ m3 = m6 ∧ m4 = 0 ∧ ¬ boolvar;mkinode(m, md, boolvar, m3, m4, m5) = mkinode(m, md1, false, m6, 0, m2)) ⊦ m1 = m6

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[m], m2, md1, m6, content0]

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[m], m2, md1, m6, content0