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Proof step 15 from proof prepost-fix-ecs (previous step)

n0 < # wlar1, n0 < # wlar1.mapIndices(nx4, λ wle. wle.ec:= n), valid-indices(wlar1, nx4), valid-indices(wlar1, nx0), valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx4) ⊦ wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0, wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0].ec:= n] = wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0, wlar1[n0].ec:= n], dups(nx0), dups(nx4), dups(nx4 + nx0), n0 ∈ nx4, n0 ∈ nx0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ valid-indices(wlar, nx) ∧ ¬ dups(nx) ∧ n < # wlar → wlar.mapIndices(nx, f0)[n] = (n ∈ nx ⊃ f0(wlar[n]);wlar[n])

Rule argument

spec: array-indices, inst: wlarray-base name: map-indices-at seq: ⊦ valid-indices(wlar, nx) ∧ ¬ dups(nx) ∧ n < # wlar → wlar.mapIndices(nx, f0)[n] = (n ∈ nx ⊃ f0(wlar[n]);wlar[n]) subst: [n, f0, nx, wlar] → [n0, λ wle. wle.ec:= n, nx4, wlar1] flags: <all paths>

Additional information

Used terms: n0, λ wle. wle.ec:= n, nx4, wlar1