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Proof step 4 from proof key-size (previous step)

(∀ a. ¬ a ∈ st) → st = ∅, ∀ a0. ¬ a0 ∈ st[a, d] ⊦ st[a, d] = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ a0. ¬ a0 ∈ st[a, d], ¬ a0 ∈ st → st = ∅ ⊦ st[a, d] = ∅

Rule argument

Additional information