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Proof step 23 from proof to-to-leq (previous step)

n0 < # x, n0 ≤ #(x to n0), ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ x to n0 to n0 = x to n0, x = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
n0 < # x, ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ x to n0 to n0 = x to n0, x = []

Rule argument

Additional information

Used simplifier rules: length-to: ¬ # x < n ⊦ #(x to n) = n;% ⊦ m ≤ m; (s)% ⊦ m < n → ¬ n < m; (s)