chore(Order/WithBot): add to_dual attributes (part 2)

[vihdzp]

Some design considerations:

• The ≤ and < instances on WithBot and WithTop are were deliberately made def-eq. I've not changed this, which results in some awkward code before we develop the API to hide this.
• There was some major disparity in the unbot and untop API. I had to add a bunch of lemmas to amend it.
• I reordered a few theorems to avoid having to constantly open and close the WithBot namespace.

---

• depends on: [Merged by Bors] - chore(Order/ConditionallyCompleteLattice): use where notation  #32635

[github-actions]

PR summary cd61ea3a12

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ PartialOrder.mk'
+ Preorder.mk'
+ WithBot.LE
+ WithBot.LT
+ WithBot.le_def
+ WithBot.lt_def
+ WithTop.le_def
+ WithTop.le_def'
+ WithTop.lt_def
+ WithTop.lt_def'
+ instance (priority := 10) WithBot.instLE : LE (WithBot α) where le := WithBot.LE
+ instance (priority := 10) WithBot.instLT : LT (WithBot α) where lt := WithBot.LT
+ instance (priority := 10) WithTop.instLE : LE (WithTop α) where le a b := WithBot.LE (α := αᵒᵈ) b a
+ instance (priority := 10) WithTop.instLT : LT (WithTop α) where lt a b := WithBot.LT (α := αᵒᵈ) b a
+ instance [PartialOrder α] : PartialOrder (WithBot α)
+ instance [Preorder α] : Preorder (WithBot α)
+ le_unbotA
+ le_unbotA_iff
+ le_unbotD
+ le_unbotD_iff
+ lt_unbotA_iff
+ lt_unbotD_iff
+ unbotA_le_iff
+ unbotA_lt_iff
+ unbotA_mono
+ unbotD_mono
+ unbot_le_unbot_iff
+ unbot_lt_unbot_iff
+ unbot_mono
- LE
- LT
- _root_.IsMin.withTop
- boundedOrder
- coe_le_coe
- coe_le_iff
- coe_lt_coe
- coe_lt_iff
- coe_lt_top
- coe_top_lt
- coe_untopD_le
- eq_of_forall_coe_le_iff
- eq_of_forall_le_coe_iff
- eq_top_iff_forall_ge
- eq_top_iff_forall_gt
- forall_coe_le_iff_le
- forall_le_coe_iff_le
- instPartialOrder
- instPreorder
- instance (priority := 10) instLE : LE (WithBot α) where le := WithBot.LE
- instance (priority := 10) instLE : LE (WithTop α) where le a b := WithBot.LE (α := αᵒᵈ) b a
- instance (priority := 10) instLT : LT (WithBot α) where lt := WithBot.LT
- instance (priority := 10) instLT : LT (WithTop α) where lt a b := WithBot.LT (α := αᵒᵈ) b a
- le_coe
- le_coe_iff
- le_iff_forall
- le_untopA_iff
- le_untopD_iff
- le_untop_iff
- lt_iff_exists
- lt_iff_exists_coe
- lt_top_iff_ne_top
- lt_untopA_iff
- lt_untopD_iff
- lt_untop_iff
- map_le_iff
- not_top_le_coe
- not_top_lt
- orderBot
- orderTop
- partialOrder
- preorder
- top_le_iff
- untopA_le
- untopA_le_iff
- untopA_lt_iff
- untopA_mono
- untopD_le
- untopD_le_iff
- untopD_lt_iff
- untopD_mono
- untop_le_iff
- untop_lt_iff
- untop_mono
-- le_def
-- lt_def

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:

• [Merged by Bors] - chore(Order/ConditionallyCompleteLattice): use where notation  #32635
  By Dependent Issues (🤖). Happy coding!