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Proof step 3 from proof to-to-leq-inf (previous step)

∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m, m ≤ n0 +1 ⊦ (nf to n0 +1) to m = nf to m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m ≤ n0 + 1, ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ (nf to n0 + 1) to m = nf to m

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2