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Proof step 3 from proof dist-add-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m0 < m ⊦ dist(m + n, m0 + n) = dist(m, m0)

Rule argument

Additional information

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