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Proof step 384 from proof refine-write_inode (previous step)

# links(m, cache_dirs) = m2, cache_files[m] = mkfile(m0, md0, m2, content), cache_files[m] = mkfile(m1, md, m2, content0), 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_files ⊦ ⟨fail#(; ; err); asynced0 := ?⟩ ((asynced0 ↔ asynced1) ∧ EFAIL = err), m ∈ cache_icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 385:
cache_files[m] = mkfile(m1, md, # links(m, cache_dirs), 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), 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_files, ¬ m ∈ cache_icache ⊦ ⟨fail#(; ; err); asynced0 := ?⟩ ((asynced0 ↔ asynced1) ∧ EFAIL = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)