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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

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];% ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)