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Proof step 9 from proof delapp (previous step)

#oc(x.first, x) + #oc(x.first, y) ≤ #oc(x.first, y -1l a), ∀ a0. #oc(a0, x) + #oc(a0, y) ≤ #oc(a0, y -1l a), ∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, x) + #oc(a0, y) ⊦ x = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
x = a1 + y0, #oc(a1, x) + #oc(a1, y) ≤ #oc(a1, y -1l a), ∀ a0. #oc(a0, x) + #oc(a0, y) ≤ #oc(a0, y -1l a), ∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, x) + #oc(a0, y) ⊦ x = []

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, a1, y0] flags:

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y; (elim) Used terms: x, a1, y0