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Proof step 10 from proof del1-01 (previous step)

ordered≤(x0), ∀ a1. ordered≤(x0 -1l a1) ⊦ a = a0, x0 = [], ordered≤(a0 ' + (x0 -1l a)), x0.first < a0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
x0 = a2 + y, ordered≤(x0), ∀ a1. ordered≤(x0 -1l a1) ⊦ a = a0, x0 = [], ordered≤(a0 ' + (x0 -1l a)), a2 < a0

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] → [x0, a2, y] flags:

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y; (elim) Used terms: x0, a2, y