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Proof step 5 from proof del-gt (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
key1 < key0, key1 < key, key ∈ ri ⊦ ((ri -- key0) |> key1)[key] = ri[key], key = key0

Rule argument

Additional information

Used simplifier rules: in-gt: ⊦ key0 ∈ ri |> key1 ↔ key0 ∈ ri ∧ key1 < key0;%at-gt: ⊦ key1 < key0 ∧ key0 ∈ ri → (ri |> key1)[key0] = ri[key0];% ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)