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Proof step 11 from proof get-last-04 (previous step)

# x = m + 1 ⊦ x[m] = x.last, x = []

User applied rule insert elim lemma

And closed the goal!

Rule argument

spec: list-last name: last-elim seq: x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a ' subst: [x, a, y] → [x, a, y]

Additional information

Used simplifier rules: get-last: ⊦ n = # x → (x + a ')[n] = a;% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ x + a ' ≠ []; (s)%x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a '; (elim) Used terms: x, a, y