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Proof step 7 from proof restrict-le1 (previous step)

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

Rule argument

Additional information

Used simplifier rules: ⊦ key < key0 → (key0 < key ↔ false); (ss)%nll: ⊦ ¬ key0 < key ∧ key0 < key1 → key < key1; (forward) from specification oelem[key-order]