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Proof step 209 from proof refine-write_inode (previous step)

# links(m, cache_dirs) = cache_files[m].nlink, cache_files[m] = mkfile(m1, md1, cache_files[m].nlink, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m2, md, cache_files[m].nlink, cache_files[m].content ⊕ mkcontent(m, cache_pcache))] ≠ (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache, 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_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, ¬ m ∈ cache_icache ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced1 ↔ asynced0) ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 210:
# links(m, cache_dirs) = m3, cache_files[m] = mkfile(m1, md1, m3, content0), cache_files[m] = mkfile(m0, md0, m3, 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), synced(cache_files, cache_icache, cache_pcache), m ∈ cache_files ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced1 ↔ asynced0) ∧ ESUCCESS = err), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m2, md, m3, content ⊕ mkcontent(m, cache_pcache))] = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache, m ∈ 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[m], m0, md0, m3, 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[m], m0, md0, m3, content