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Proof step 2 from proof firstN-empty (previous step)

firstn(n, x) = [] ⊦ n = 0

User applied rule structural induction

And closed the goal!

Rule argument

indvar: n

Additional information

Used simplifier rules: firstN-rec: ⊦ firstn(n + 1, x) = x.first + firstn(n, x.rest);%nat freely generated by 0, +1;;%succ: ⊦ m +1 = m + 1; from specification nat-basic2%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%app-02-ant: ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list