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Proof step 3 from proof refine-lookup (previous step)

dent = dent0, err = err0, 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 ⊦ ⟪cache_lookup#(p_ino, cache_dirs, cache_files, cache_asynced; dent, err, cache_dcache)⟫ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (dent = dent0 ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 4:
asynced0 ↔ cache_asynced, dcache = cache_dcache, dent = dent0, dirs = cache_dirs, err = err0, 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), p_ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪if pre-lookup(p_ino, dent, dirs, files) then let asynced = false, name = dent.name in {dcache_get#(p_ino, name, dcache; asynced, dent, err); if ¬ asynced ∨ err ≠ ESUCCESS then {afs_lookup#(p_ino, dirs, files, asynced0; dent, err); if err = ESUCCESS then dcache_set#(p_ino, name, dent; err, dcache)}} else abort⟫ ⟨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: cache_lookup#(P_INO, DIRS, FILES, ASYNCED; DENT, ERR, DCACHE) {if pre-lookup(P_INO, DENT, DIRS, FILES) then let HIT = false, NAME = DENT.name in {dcache_get#(P_INO, NAME, DCACHE; HIT, DENT, ERR); if ¬ HIT ∨ ERR ≠ ESUCCESS then {afs_lookup#(P_INO, DIRS, FILES, ASYNCED; DENT, ERR); if ERR = ESUCCESS then dcache_set#(P_INO, NAME, DENT; ERR, DCACHE)}} else abort };