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Proof step 5 from proof deln-le (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-le: ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0;%at-le: ⊦ ¬ 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)