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Proof step 2 from proof firstn-firstn (previous step)

m ≤ n, n ≤ # x, m ≤ # x ⊦ firstn(m, firstn(n, x)) = firstn(m, x)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n, x. m0 ≤ n ∧ n ≤ # x ∧ m0 ≤ # x → firstn(m0, firstn(n, x)) = firstn(m0, x), m0 +1 ≤ n, n ≤ # x, m0 +1 ≤ # x ⊦ firstn(m0 +1, firstn(n, x)) = firstn(m0 +1, x)

Rule argument

indvar: m

Additional information

Used simplifier rules: firstN-zero: ⊦ firstn(0, x) = [];%nat freely generated by 0, +1;;