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Proof step 5 from proof inv-lookup (previous step)

afs-cons(dirs, files), p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪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}⟫ true

Heuristic conditional right split applied rule if right

And obtained the following new goals

Proof step 6:
afs-cons(dirs, files), dent.name ∈ dirs[p_ino].entries, p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS⟫ true
Proof step 8:
afs-cons(dirs, files), p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dent := negdentry(dent.name); err := ENOENT⟫ true, dent.name ∈ dirs[p_ino].entries

Proof step 5 from proof inv-lookup (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

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