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Proof step 7 from proof refine-lookup (previous step)

¬ asynced, dent = dent0, err = err0, 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), p_ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dcache_get#(p_ino, dent0.name, cache_dcache; asynced, dent, err); if ¬ asynced ∨ err ≠ ESUCCESS then {afs_lookup#(p_ino, cache_dirs, cache_files, cache_asynced; dent, err); if err = ESUCCESS then dcache_set#(p_ino, dent0.name, dent; err, cache_dcache)}⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 8:
¬ asynced, dcache = cache_dcache, dent = dent0, err = err0, name = dent0.name, 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), p_ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪let key = dentrykey(p_ino, name) in if key ∈ dcache then {dent := dcache[key]; asynced := true} else asynced := false; err := ESUCCESS; if ¬ asynced ∨ err ≠ ESUCCESS then {afs_lookup#(p_ino, cache_dirs, cache_files, cache_asynced; dent, err); if err = ESUCCESS then dcache_set#(p_ino, dent0.name, dent; err, cache_dcache)}⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: dcache_get#(P_INO, NAME, DCACHE; HIT, DENT, ERR) {let KEY = dentrykey(P_INO, NAME) in if KEY ∈ DCACHE then {DENT := DCACHE[KEY]; HIT := true} else HIT := false; ERR := ESUCCESS };