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

# x = m + 1 ⊦ x = [], x[m] = x.last

User applied rule insert elim lemma

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: get-last: ⊦ n = # x → (x + a ')[n] = a;%len: ⊦ #(x + y) = # x + # y; from specification list%len-02: ⊦ # a ' = 0 +1; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%e-02: ⊦ x + a ' ≠ []; from specification list%x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a '; (elim) Used terms: x, a, y