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Proof step 4 from proof refine-sync (previous step)

asynced ↔ cache_asynced, dirs = cache_dirs, 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_sync#(dirs, files; ; asynced, err)⟫ ⟨afs_sync#(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; ; afs_asynced, err0)⟩ ((afs_asynced ↔ asynced) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 5:
asynced ↔ cache_asynced, dirs = cache_dirs, files = cache_files, 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) ⊦ ⟪fail_or_success#(; ; err); asynced := err = ESUCCESS⟫ ⟨afs_sync#(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; ; afs_asynced, err0)⟩ ((afs_asynced ↔ asynced) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_sync#(DIRS, FILES; ; ASYNCED, ERR) {fail_or_success#(; ; ERR); ASYNCED := ERR = ESUCCESS};