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Proof step 29 from proof inv-lookup (previous step)

dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), p_ino ∈ dirs, dent.name ∈ entries, ¬ dentrykey(p_ino, dent.name) ∈ dcache, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dcache_set#(p_ino, dent.name, mkdentry(dent.name, entries[dent.name]); err, dcache)⟫ dcache-cons(dcache, dirs, files)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 30:
dirs[p_ino] = mkdir(m, md, # links(p_ino, dirs), m1, entries), dent = mkdentry(dent0.name, entries[dent0.name]), err = ESUCCESS, name = dent0.name, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), dent0.name ∈ entries, p_ino ∈ dirs, asynced1 → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪let key = dentrykey(p_ino, name) in dcache[key] := dent⟫ dcache-cons(dcache, dirs, files), dentrykey(p_ino, dent0.name) ∈ dcache

Rule argument

pos: right 1

Additional information

Used simplifier rules: dcache_set#(P_INO, NAME, DENT; ERR, DCACHE) {let KEY = dentrykey(P_INO, NAME) in DCACHE[KEY] := DENT};