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Proof step 5 from proof to-to-leq (previous step)

m ≤ n, n ≤ # x, m ≤ # x ⊦ x to n to m = x to m

User applied rule structural induction

And obtained the following new goals

Proof step 6:
m ≤ # x, n0 +1 ≤ # x, m ≤ n0 +1, ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ x to n0 +1 to m = x to m

Rule argument

indvar: n

Additional information

Used simplifier rules: to-zero-l: ⊦ x to 0 = [];%nat freely generated by 0, +1;;% ⊦ m ≤ 0 ↔ m = 0; (s)% ⊦ 0 ≤ m; (s)