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Proof step 6 from proof to-from-01 (previous step)

n ≤ # x0, ∀ n. n < # x0 → (x0 to n) from n = [] ∨ x0 = [] ⊦ (a ' + x0 to n) from n = []

User applied rule structural induction

And obtained the following new goals

Proof step 7:
∀ x0, a. n0 ≤ # x0 ∧ (∀ n. n < # x0 → (x0 to n) from n = [] ∨ x0 = []) → (a ' + x0 to n0) from n0 = [], n0 +1 ≤ # x0, ∀ n. n < # x0 → (x0 to n) from n = [] ∨ x0 = [] ⊦ (a ' + x0 to n0 +1) from n0 +1 = []

Rule argument

indvar: n

Additional information

Used simplifier rules: to-zero-l: ⊦ x to 0 = [];%from-zero-l: ⊦ x from 0 = x;%nat freely generated by 0, +1;;