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

⊦ key1 < key0, ∀ key. (key ∈ (ri -- key0) |> key1 ↔ key ∈ ri |> key1) ∧ (key ∈ (ri -- key0) |> key1 → ((ri -- key0) |> key1)[key] = (ri |> key1)[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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];%nll: ⊦ ¬ key0 < key ∧ key0 < key1 → key < key1; (forward) from specification oelem[key-order]% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)