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Proof step 18 from proof prepost-fix-ecs (previous step)

valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx4), valid-indices(wlar1, nx4), valid-indices(wlar1, nx0), # wlar1.mapIndices(nx4, λ wle. wle.ec:= n) ≤ nx0.head ⊦ nx0 = [], dups(nx4 + nx0), dups(nx4), dups(nx0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: list-data, inst: nat-list-set name: elim-list-c seq: nx ≠ [] ⊦ n = nx.head ∧ nx0 = nx.tail ↔ nx = n + nx0 subst: [nx, n, nx0] → [nx0, n0, nx]

Additional information

Used simplifier rules: nx ≠ [] ⊦ n = nx.head ∧ nx0 = nx.tail ↔ nx = n + nx0; (elim) Used terms: nx0, n0, nx