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Proof step 8 from proof dist-add-01 (previous step)

m + n ≤ m0 + n ⊦ m0 + n - m + n = dist(m, m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m ≤ m0 ⊦ m0 - m = dist(m, m0)

Rule argument

Additional information

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