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Proof step 91 from proof refine-lookup (previous step)

dent = dent0, 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, ⌊err0⌋ , ¬ dentrykey(p_ino, dent0.name) ∈ cache_dcache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err1)⟩ (dent = dent0 ∧ err0 = err1)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 92:
asynced ↔ cache_asynced, dent = dent0, dent1 = dent0, dirs = cache_dirs, err = err1, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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, ⌊err0⌋ , 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 { if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT} or fail#(; ; err)} else abort⟩ (dent1 = dent ∧ err0 = err), dentrykey(p_ino, dent0.name) ∈ cache_dcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_lookup#(P_INO, DIRS, FILES, ASYNCED; DENT, ERR) {if pre-lookup(P_INO, DENT, DIRS, FILES) then { if DENT.name ∈ DIRS[P_INO].entries then {DENT := mkdentry(DENT.name, DIRS[P_INO].entries[DENT.name]); ERR := ESUCCESS} else {DENT := negdentry(DENT.name); ERR := ENOENT} or fail#(; ; ERR)} else abort };