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Proof step 20 from proof prepost-fix-ecs (previous step)

# wlar1.mapIndices(nx4, λ wle. wle.ec:= n) < # wlar1, n0 < # wlar1, valid-indices(wlar1, nx1), valid-indices(wlar1, nx4), valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx4), # wlar1.mapIndices(nx4, λ wle. wle.ec:= n) ≤ n0 ⊦ dups(nx1), dups(nx4), dups(nx4 + nx1), n0 ∈ nx1, n0 ∈ nx4

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: λ wle. wle.ec:= n, nx4, wlar1