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Proof step 3 from proof refine-check-commit (previous step)

err = err0, 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), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_check_commit#(cache_dirs, cache_files; err, cache_asynced)⟫ ⟨afs_check_commit#(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; err0; afs_asynced)⟩ ((afs_asynced ↔ cache_asynced) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 4:
asynced ↔ cache_asynced, dirs = cache_dirs, err = err0, files = cache_files, 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), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_check_commit#(dirs, files; err; asynced)⟫ ⟨afs_check_commit#(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; err0; afs_asynced)⟩ ((afs_asynced ↔ asynced) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_check_commit#(DIRS, FILES; ERR, ASYNCED) {afs_check_commit#(DIRS, FILES; ERR; ASYNCED)};