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Proof step 2 from proof min-first (previous step)

n0 ≤ n1, n0 ≤ n2 ⊦ min(n0, n1, n2) = n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ min(n0, n1, n2) = min(n0, min(n1, n2))
Proof step 4:
n0 ≤ n2, n0 ≤ n1 ⊦ min(n0, min(n1, n2)) = n0

Rule argument

Additional information

Used simplifier rules: min3: ⊦ min(n0, n1, n2) = min(n0, min(n1, n2));