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Proof step 39 from proof refine-fsync (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, cache_files0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files0), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache0, cache_dirs, cache_files0), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files0), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache0, cache_pcache0), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files0, cache_icache0, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache), err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ⟨fail_or_success#(; ; err); choose bv with true in asynced0 := bv⟩ ((asynced0 ↔ cache_asynced) ∧ err1 = err)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 40:
cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, cache_files0), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files0), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons(cache_icache0, cache_dirs, cache_files0), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files0), synced(cache_dirs, cache_icache, cache_pcache), synced(cache_dirs, cache_icache0, cache_pcache0), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced(cache_files0, cache_icache0, cache_pcache0), err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ⟨choose err0 with ⌊err0⌋ ∨ err0 = ESUCCESS in err := err0; choose bv with true in asynced0 := bv⟩ ((asynced0 ↔ cache_asynced) ∧ err1 = err)

Rule argument

pos: right 1

Additional information

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