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Proof step 10 from proof prepost-fix-ecs (previous step)

nx2.head < # wlar1.mapIndices(nx4, λ wle. wle.ec:= n), valid-indices(wlar1, nx2), valid-indices(wlar1, nx4), valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx4) ⊦ nx2 = [], dups(nx2), dups(nx4), dups(nx4 + nx2), ∃ nx. nx4 + nx2 = nx + nx2.tail ∧ wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[nx2.head, wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[nx2.head].ec:= n] = wlar1.mapIndices(nx, λ wle. wle.ec:= n) ∧ valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx)

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] → [nx2, n0, nx0]

Additional information

Used simplifier rules: nx ≠ [] ⊦ n = nx.head ∧ nx0 = nx.tail ↔ nx = n + nx0; (elim) Used terms: nx2, n0, nx0