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Proof step 16 from proof to-to-leq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
n0 < # x, ∀ m, x. m ≤ n0 ∧ n0 ≤ # x ∧ m ≤ # x → x to n0 to m = x to m ⊦ x = [], ((x to n0) + x[n0] ' to n0) + x[n0] ' = x to n0 + 1

Rule argument

Additional information

Used simplifier rules: length-to: ¬ # x < n ⊦ #(x 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%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1