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Proof step 1 from proof lr-03 (conclusion)

⊦ x ≠ [] ∧ y ≠ [] → (# x.rest = # y.rest ↔ # x = # y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ y = [], x = [], # x - 1 = # y - 1 ↔ # x = # y

Rule argument

Additional information

Used simplifier rules: length-rest: ⊦ x ≠ [] → # x.rest = (# x)-1;%pred-03: ⊦ n -1 = n - 1; from specification nat