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Proof step 2 from proof add-cancel-num-04 (previous step)

⊦ n < m → (⌜n⌝ + n∞1 = ⌜m⌝ + n∞2 ↔ n∞1 = ⌜m - n⌝ + n∞2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < m ⊦ ⌜n⌝ + n∞1 = ⌜m⌝ + n∞2 ↔ n∞1 = ⌜m - n⌝ + n∞2, m = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1