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Proof step 5 from proof refine-fsyncdir (previous step)

asynced ↔ cache_asynced, asynced0 ↔ asynced1, 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)⟫ ⟨afs_fsyncdir#(inode, asynced1, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; ; err0)⟩ (err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 6:
asynced0 ↔ asynced1, 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) ⊦ ⟪choose err0 with ⌊err0⌋ ∨ err0 = ESUCCESS in err := err0⟫ ⟨afs_fsyncdir#(inode, asynced1, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; ; err0)⟩ (err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail_or_success#(; ; ERR) {choose ERR0 with ⌊ERR0⌋ ∨ ERR0 = ESUCCESS in ERR := ERR0};