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Proof step 4 from proof rest-app (previous step)

n0 ≤ # y ⊦ restn(n0 + # x, x + y) = restn(n0, y)

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ n0, y. n0 ≤ # y → restn(n0 + # x0, x0 + y) = restn(n0, y), n0 ≤ # y ⊦ restn(n0 + #(a + x0), (a + x0) + y) = restn(n0, y)

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list