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Proof step 10 from proof refine-sync (previous step)

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), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨afs_sync#(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; ; afs_asynced, err1)⟩ ((afs_asynced ↔ err0 = ESUCCESS) ∧ err0 = err1)

User applied rule call right

And obtained the following new goals

Proof step 11:
dirs = cache_dirs, files = (cache_files ⊕ 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_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨fail_or_success#(; ; err); asynced := err = ESUCCESS⟩ ((asynced ↔ err0 = ESUCCESS) ∧ err0 = err)

Rule argument

pos: right 1

Additional information

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