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Proof step 6 from proof dist-add-01 (previous step)

m0 + n < m + n, m0 < m ⊦ m + n - m0 + n = dist(m, m0), m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m0 < m ⊦ m = 0, m - m0 = dist(m, m0)

Rule argument

Additional information

Used simplifier rules: l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%cancel-01: ⊦ m + n - n + n1 = m - n1; from specification nat