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Proof step 1 from proof min-add-same (conclusion)

⊦ min(n + n0, n + n1) = n + min(n0, n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ min(n, m) = (n < m ⊃ n;m)
Proof step 3:
⊦ (n0 < n1 ⊃ n + n0;n + n1) = n + (n0 < n1 ⊃ n0;n1)

Rule argument

Additional information

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