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Proof step 8 from proof Del-notin (previous step)

a ∈ (st0 -- a)[a0, d], ∀ a. ¬ a ∈ st0 -- a ⊦ a = a0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
a ∈ st0 -- a, ∀ a. ¬ a ∈ st0 -- a ⊦ a = a0

Rule argument

Additional information

Used simplifier rules: in-neq: ⊦ a ≠ b → (a ∈ st[b, d] ↔ a ∈ st);