feat: colex order on (dependent) finsupps

[vihdzp]

---

• depends on: feat: CoeFun for Lex and Colex #30481
• depends on: [Merged by Bors] - feat: group instances on Colex α #30483
• depends on: [Merged by Bors] - fix: remove second type from test in order.lean  #30510

[github-actions]

PR summary 50803f90cd

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ Colex.addLeftMono
+ Colex.addLeftStrictMono
+ Colex.addRightMono
+ Colex.addRightStrictMono
+ Colex.instPow
+ Colex.instPow'
+ Colex.isOrderedAddMonoid
+ Colex.isOrderedCancelAddMonoid
+ Colex.isStrictOrder
+ Colex.isTotalLE
+ Colex.linearOrder
+ Colex.orderBot
+ Colex.partialOrder
+ Lex.isTotalLE
+ colex_lt_iff
+ instance [LT ι] [∀ i, LT (α i)] : LT (Colex (Π₀ i, α i))
+ instance [Mul α] [IsCancelMul α] : IsCancelMul (Colex α)
+ instance [Mul α] [IsLeftCancelMul α] : IsLeftCancelMul (Colex α)
+ instance [Mul α] [IsRightCancelMul α] : IsRightCancelMul (Colex α)
+ instance [h : CancelCommMonoid α] : CancelCommMonoid (Colex α) := h
+ instance [h : CancelMonoid α] : CancelMonoid (Colex α) := h
+ instance [h : CommGroup α] : CommGroup (Colex α) := h
+ instance [h : CommMonoid α] : CommMonoid (Colex α) := h
+ instance [h : CommSemigroup α] : CommSemigroup (Colex α) := h
+ instance [h : Div α] : Div (Colex α) := h
+ instance [h : DivInvMonoid α] : DivInvMonoid (Colex α) := h
+ instance [h : DivisionCommMonoid α] : DivisionCommMonoid (Colex α) := h
+ instance [h : DivisionMonoid α] : DivisionMonoid (Colex α) := h
+ instance [h : Group α] : Group (Colex α) := h
+ instance [h : Inv α] : Inv (Colex α) := h
+ instance [h : InvolutiveInv α] : InvolutiveInv (Colex α) := h
+ instance [h : LeftCancelMonoid α] : LeftCancelMonoid (Colex α) := h
+ instance [h : LeftCancelSemigroup α] : LeftCancelSemigroup (Colex α) := h
+ instance [h : Monoid α] : Monoid (Colex α) := h
+ instance [h : Mul α] : Mul (Colex α) := h
+ instance [h : MulOneClass α] : MulOneClass (Colex α) := h
+ instance [h : One α] : One (Colex α) := h
+ instance [h : RightCancelMonoid α] : RightCancelMonoid (Colex α) := h
+ instance [h : RightCancelSemigroup α] : RightCancelSemigroup (Colex α) := h
+ instance [h : Semigroup α] : Semigroup (Colex α) := h
+ instance {α γ} [H : CoeFun α γ] : CoeFun (Colex α) γ
+ instance {α γ} [H : CoeFun α γ] : CoeFun (Lex α) γ
+ lex_lt_iff
+ ofColex_apply
+ ofColex_div
+ ofColex_eq_one
+ ofColex_inv
+ ofColex_mul
+ ofColex_one
+ ofColex_pow
+ pow_ofColex
+ pow_toColex
+ toColex_apply
+ toColex_div
+ toColex_eq_one
+ toColex_inv
+ toColex_monotone
+ toColex_mul
+ toColex_one
+ toColex_pow

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat: CoeFun for Lex and Colex #30481
• [Merged by Bors] - feat: group instances on Colex α #30483
• [Merged by Bors] - fix: remove second type from test in order.lean  #30510
  By Dependent Issues (🤖). Happy coding!