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Proof step 5 from proof toSet-subseteq-domri-notin (previous step)

key ∈ kx, ∀ key. key ∈ kx.toSet → key ∈ dom ri ⊦ key ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
key ∈ kx, ∀ key0. key0 ∈ kx → key0 ∈ ri ⊦ key ∈ ri

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ dom ri ↔ key ∈ ri; (s)% ⊦ key ∈ kx.toSet ↔ key ∈ kx; (s)