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Proof step 7 from proof restrict-le3 (previous step)

key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key ⊦ key0 < key1, (key ∈ ri ∧ ¬ key1 < key → ¬ key0 < key) ∧ (key ∈ ri ∧ ¬ key0 < key ∧ ¬ key1 < key → (ri |≤ key0 |≤ key1)[key] = ri[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
key ∈ ri ⊦ (ri |≤ key0 |≤ key1)[key] = ri[key], key0 < key1, key1 < key, key0 < key

Rule argument

Additional information

Used simplifier rules: nnn: ⊦ ¬ key1 < key0 ∧ ¬ key < key1 → ¬ key < key0; (forward) from specification oelem[key-order]