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Proof step 1 from proof below-rem-in (conclusion)

n > m ⊦ below(ns -- m, n) = below(ns, n) -- m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m < n ⊦ below(ns -- m, n) = below(ns, n) -- m

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m > n ↔ n < m; (s)