feat: IsBotOneClass and IsBotZeroClass

[vihdzp]

We create typeclasses expressing that 0 or 1 is a bottom element in a type. We use this to unify and generalize various theorems which are currently stated for canonically ordered monoids.

See Zulip.

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• depends on: chore: make argument in zero_le/one_le implicit #38148

[github-actions]

PR summary b9cac30121

Import changes exceeding 2%

%	File
+2.56%	Mathlib.Algebra.Order.Monoid.Canonical.Defs
+4.44%	Mathlib.Algebra.Order.Monoid.Unbundled.Basic
+4.15%	Mathlib.Order.Interval.Set.Basic

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Order.Monoid.Unbundled.Basic	180	188	+8 (+4.44%)
Mathlib.Order.Interval.Set.Basic	193	201	+8 (+4.15%)
Mathlib.Algebra.Order.Monoid.Canonical.Defs	195	200	+5 (+2.56%)
Mathlib.Algebra.Order.Sub.Basic	221	225	+4 (+1.81%)
Mathlib.Algebra.Order.BigOperators.Group.List	343	347	+4 (+1.17%)
Mathlib.Algebra.Order.Group.Indicator	305	307	+2 (+0.66%)
Mathlib.Algebra.Order.Kleene	411	413	+2 (+0.49%)
Mathlib.Dynamics.PeriodicPts.Defs	519	521	+2 (+0.39%)
Mathlib.Algebra.Order.BigOperators.Group.Finset	542	544	+2 (+0.37%)
Mathlib.Order.SuccPred.LinearLocallyFinite	561	563	+2 (+0.36%)
Mathlib.Combinatorics.Enumerative.Composition	671	673	+2 (+0.30%)

Import changes for all files

Files	Import difference
../mathlib-ci/scripts/pr_summary/import_trans_difference.sh all
There are 6740 files with changed transitive imports taking up over 303649 characters: this is too many to display!
You can run this locally from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

---

Declarations diff

+ IsBotOneClass
+ IsBotZeroClass
+ LT.lt.ne_one
+ instance (priority := 10) of_gt' [Preorder α] [IsBotZeroClass α] [One α]
+ instance (priority := 100) [LE α] [Zero α] [One α] [IsBotZeroClass α] : ZeroLEOneClass α
+ instance : IsBotOneClass α
+ instance : IsBotZeroClass (WithZero α)
+ ne_one_of_lt
- LT.lt.pos
- Ne.pos
- instance (priority := 10) of_gt' {M : Type*} [AddZeroClass M] [Preorder M] [CanonicallyOrderedAdd M]
- instance (priority := 100) LinearOrderedCommMonoidWithZero.toZeroLeOneClass : ZeroLEOneClass α
- ne_zero_of_lt

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

---

No changes to technical debt.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib-dependent-issues]

This PR/issue depends on:

• chore: make argument in zero_le/one_le implicit #38148
  By Dependent Issues (🤖). Happy coding!