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Proof step 1 from proof insert-02 (conclusion)

⊦ a ∈ s ∧ ¬ b ∈ s → st[a, d][b] = st[b]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ∈ s ⊦ s = ∅, st[a, d][b] = st[b], # s = 0, b ∈ s

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ s ≠ ∅ → # s ≠ 0; (forward) from specification set-basic%ne-01: ⊦ a ∈ s → s ≠ ∅; (forward) from specification set-basic