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Proof step 1 from proof firstn-app (conclusion)

⊦ firstn(# x + n, x + y) = x + firstn(n, y)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ n, y. firstn(# x0 + n, x0 + y) = x0 + firstn(n, y) ⊦ firstn(#(a + x0) + n, (a + x0) + y) = (a + x0) + firstn(n, 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