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Proof step 2 from proof ole-last-01 (previous step)

ordered≤(x) ⊦ ordered≤(x + a ') ↔ ¬ a < x.last, x = []

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, a0, y] flags:

Additional information

Used simplifier rules: ole-last: ⊦ ordered≤(x + a ') → (ordered≤(x + a ' + b ') ↔ ¬ b < a);%a: ⊦ (x + y) + z = x + y + z; from specification list%x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a '; (elim) Used terms: x, a0, y