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Proof step 2 from proof postfix-rest-01 (previous step)

x ⊒ y ⊦ x = [], x.rest ⊒ y

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: list-data inst: name: elim-list-c seq: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y subst: [x, a, y] → [x, a, y0] flags:

Additional information

Used simplifier rules: postfix-one-less: ⊦ a ' + x ⊒ y → (¬ x ⊒ y ↔ false);%c: ⊦ a + x = a ' + x; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y; (elim) Used terms: x, a, y0