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

lastn(n, x) = [] ⊦ n = 0

User applied rule structural induction

And closed the goal!

Rule argument

indvar: n

Additional information

Used simplifier rules: lastN-rec: ⊦ lastn(n + 1, x) = lastn(n, x.butlast) + x.last;%nat freely generated by 0, +1;;%succ: ⊦ m +1 = m + 1; from specification nat-basic2%Last: ⊦ x + a = x + a '; 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