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Proof step 10 from proof ordered-postfix (previous step)

x ⊒ a ' + x1, ordered≤(x1), ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ x1 = [], ordered≤(x), x1.first < a

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
x1 = a0 + y, x ⊒ a ' + x1, ordered≤(x1), ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ x1 = [], ordered≤(x), a0 < a

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] → [x1, a0, y] flags:

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y; (elim) Used terms: x1, a0, y