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Proof step 3 from proof cancel-01 (previous step)

⊦ n + n1 ≤ m + n, m + n - n + n1 = m - n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m < n1 ⊦ m + n - n + n1 = m - n1, n1 = 0

Rule argument

Additional information

Used simplifier rules: lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0;%lels-01: ⊦ ¬ m ≤ n ↔ n < m;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2