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Proof step 17 from proof to-to-leq-inf (previous step)

¬ n0 < #(nf to n0), ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) to n0) + nf(n0) '[n0 - #(nf to n0)] ' = nf to n0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) to n0) + nf(n0) ' = nf to n0 + 1

Rule argument

Additional information

Used simplifier rules: size-inf-to: ⊦ #(nf to n) = n;%ler: ⊦ m ≤ m; from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%one-03: ⊦ a '[0] = a; from specification list-del%zero: ⊦ m - m = 0; from specification nat