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Proof step 22 from proof to-to-leq-inf (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
m ≤ n0 + 1, m ≤ n0, ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ (nf to n0) to m = nf to m

Rule argument

Additional information

Used simplifier rules: size-inf-to: ⊦ #(nf to n) = n;