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Proof step 3 from proof butlast-eq (previous step)

x.butlast + a ' = x, a ∈ x ⊦ a = x.last, x = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a '

Rule argument

spec: <toplevel> name: last-elim seq: x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a ' subst: [x, a, y] → [x, a0, y]

Additional information

Used simplifier rules: ⊦ x + y = x + z ↔ y = z; (s)% ⊦ a ' = b ' ↔ a = b; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x, a0, y