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Proof step 1 from proof rm-size-04 (conclusion)

⊦ # rmdup(x + y + z) ≤ # rmdup(x + z) → # rmdup(x + y + z) = # rmdup(x + z)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# rmdup(x + y + z) < # rmdup(x + z) ⊦ # rmdup(x + y + z) = # rmdup(x + z), x + z = []

Rule argument

Additional information

Used simplifier rules: rm-empty: ⊦ rmdup(x) = [] ↔ x = [];%l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat