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Proof step 5 from proof key-size (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 1 terms: a

Additional information

Used simplifier rules: In-insert: ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st; Used terms: a