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Proof step 4 from proof prepost-fix-ecs (previous step)

nx0 = nx, nx1 = nx, wlar0 = wlar, valid-indices(wlar, nx) ⊦ dups(nx), ∃ nx. nx0 = nx + nx0 ∧ wlar = wlar.mapIndices(nx, λ wle. wle.ec:= n) ∧ valid-indices(wlar, nx) ∧ ¬ dups(nx0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
valid-indices(wlar, nx) ⊦ dups(nx), valid-indices(wlar, [])

Rule argument

Additional information

Used simplifier rules: ⊦ wlar.mapIndices([], f0) = wlar; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ nx = nx0 + nx ↔ nx0 = []; (s)