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Proof step 4 from proof ols-rec (previous step)

x = a + y ⊦ ordered<(x) ↔ a < y.head ∧ ordered<(y), x = [], y = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ ordered<(a ' + y) ↔ a < y.head ∧ ordered<(y), y = []

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)% ⊦ a + x = a ' + x; (s)