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Proof step 8 from proof dist-c (previous step)

m = n0 + n, n < m, n ≤ m ⊦ n0 = dist(n, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ n0 = dist(n, n0 + n), n0 = 0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)