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Proof step 18 from proof to-to-leq-inf (previous step)

∀ 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, n0 < #(nf to n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
∀ 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;% ⊦ m ≤ m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ a '[0] = a; (s)% ⊦ m - m = 0; (s)