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Proof step 1 from proof btwo (conclusion)

⊦ (a ' + b ' + x).butlast = a ' + (b ' + x).butlast

User applied rule insert elim lemma

And obtained the following new goals

Proof step 2:
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] → [b ' + x, a0, y] flags: rewrite, current

Additional information

Used simplifier rules: butlast-def: ⊦ (x + a ').butlast = x;%e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%app-02-ant: ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list Used terms: b ' + x, a0, y