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

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

User applied rule call right

And obtained the following new goals

Proof step 5:
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)

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_fsyncdir#(INODE, ISDATASYNC, DIRS, FILES, ASYNCED; ; ERR) {fail_or_success#(; ; ERR)};