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Proof step 8 from proof prefixn-butlast (previous step)

# y = m + 1 ⊦ y + z = [], y.butlast = firstn(m, y + z)

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] → [y, a, y0]

Additional information

Used simplifier rules: ⊦ #(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 ' + y ≠ []; (s)% ⊦ firstn(# x, x + y) = x; (s)% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a '; (elim) Used terms: y, a, y0