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Proof step 3 from proof ols-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ y = [], ordered<(a ' + y) ↔ a < y.first ∧ ordered<(y)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%c: ⊦ a + x = a ' + x; from specification list