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Proof step 2 from proof inv-lookup (previous step)

afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-lookup(p_ino, dent, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache) ⊦ ⟪cache_lookup#(p_ino, dirs, files, asynced0; dent, err, dcache)⟫ dcache-cons(dcache, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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, asynced → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪cache_lookup#(p_ino, dirs, files, asynced0; dent, err, dcache)⟫ dcache-cons(dcache, dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)