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Proof step 3 from proof last-ex (previous step)

a ∈ x ⊦ a = x.last, ∃ y, z. x = y + a ' + z ∧ z ≠ []

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 '
Proof step 5:
x = y0 + a0 ', a ∈ x ⊦ a = a0, x = [], ∃ y, z. x = y + a ' + z ∧ z ≠ []

Rule argument

spec: <toplevel> name: last-elim seq: x ≠ [] ⊦ a = x.last ∧ y = x.butlast ↔ x = y + a ' subst: [x, a, y] → [x, a0, y0] flags: <rotated> <all paths>

Additional information

Used simplifier rules: ⊦ ¬ a ∈ []; (s) Used terms: x, a0, y0