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Proof step 2 from proof butlast-eq (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a '

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: current, []

Additional information

Used simplifier rules: app-06: ⊦ x + a ' = y + b ' ↔ x = y ∧ a = b; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x, a0, y