This issue is similar to a bug where `isDefEqOffset` was exposing
`Nat.add` when processing `HAdd.hAdd`.
Fixes#561
The example at issue #561 is now working, but we may have other places
where raw literals are being accidentally exposed.
We need this refinement to be able to process the following example.
```
import Mathlib.RingTheory.Nullstellensatz
import Mathlib.PostPort.Coe
namespace MvPolynomial.Fun
open Ideal
variable {k : Type u} [instField : Field k]
variable {σ : Type v}
variable [instIAC : IsAlgClosed k] [instF : Fintype σ]
(@Ideal.{max v u}
(@MvPolynomial.{v, u} σ k
(@CommRingS.toCommSemiring.{u} k
(@EuclideanDomain.toCommRing.{u} k (@Field.toEuclideanDomain.{u} k instField))))
(@RingS.toSemiring.{max v u}
(@MvPolynomial.{v, u} σ k
(@CommRingS.toCommSemiring.{u} k
(@EuclideanDomain.toCommRing.{u} k (@Field.toEuclideanDomain.{u} k instField))))
(@Domain.toRing.{max v u}
(@MvPolynomial.{v, u} σ k
(@CommRingS.toCommSemiring.{u} k
(@EuclideanDomain.toCommRing.{u} k (@Field.toEuclideanDomain.{u} k instField))))
(@IntegralDomain.toDomain.{max v u}
(@MvPolynomial.{v, u} σ k
(@CommRingS.toCommSemiring.{u} k
(@EuclideanDomain.toCommRing.{u} k (@Field.toEuclideanDomain.{u} k instField))))
(@MvPolynomial.integralDomain.{u, v} k σ (@Field.toIntegralDomain.{u} k instField))))))
```
This example was extracted from a failure at
```
theorem vanishing_ideal_zero_locus_eq_radical (I : Ideal (MvPolynomial σ k)) : vanishingIdeal (ZeroLocus I) = I.radical
```
Try to improve the performance issue described at #587.
The issue is that Mathlib contains thousands of theorems where the
associated key for the discrimination tree is just
`Key.other`. The indexing is not effective for them. This happens because
1- Lambda expressions are indexed using `Key.other`. The
discrimination tree mainly focus on the first-order structure.
2- It unfolds reducible constants when inserting and retrieving
entries. The motivation is that users expect simp theorems to fire
modulo reducible constants.
Then, we have many theorems such as
```lean
map ?g ∘ map ?f = map (?g ∘ ?f)
```
when we expand the function composition on the left-hand side, we get
```lean
fun (x : List ?α) => map ?g (map ?f x)
```
Which is indexed as `Key.other`.
We should not avoid the `Array`s in the discrimination tree nodes
If the index is working effectively, these arrays are all very small.
In this commit, we try to address the problem by using a different
approach. When processing the root of a pattern, we interrupt
reduction as soon as the we hit something that would be indexed
as `Key.other`. Note that, in Lean 3, the root of a pattern also
receives special treatment.
