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Proof step 1 from proof restn-empty (conclusion)

⊦ n ≤ # x → (restn(n, x) = [] ↔ n = # x)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ n. n ≤ # x0 → (restn(n, x0) = [] ↔ n = # x0) ⊦ n ≤ #(a + x0) → (restn(n, a + x0) = [] ↔ n = #(a + x0))

Rule argument

indvar: x

Additional information

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