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Proof step 2 from proof append-from-le (previous step)

n ≤ # x ⊦ x + y from n = (x from n) + y

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n, y. n ≤ # x0 → x0 + y from n = (x0 from n) + y, n ≤ #(a + x0) ⊦ (a + x0) + y from n = (a + x0 from n) + y

Rule argument

indvar: x

Additional information

Used simplifier rules: from-zero-l: ⊦ x from 0 = x;%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%size-01: ⊦ # [] = 0; from specification list-data%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat