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Proof step 7 from proof firstN-lastN (previous step)

# x = n0 + n ⊦ firstn(n0, x) + restn(n0, x) = x

User applied rule structural induction

And obtained the following new goals

Proof step 8:
∀ n0, n. # x0 = n0 + n → firstn(n0, x0) + restn(n0, x0) = x0, #(a + x0) = n0 + n ⊦ firstn(n0, a + x0) + restn(n0, a + x0) = a + x0

Rule argument

indvar: x

Additional information

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