feat(Order/RelIso): add theorems about RelHom.comp and RelEmbedding.trans

[IvanRenison]

Co-authored-by: SnirBroshi 26556598+SnirBroshi@users.noreply.github.com

---

Missing of this theorems noticed by @SnirBroshi in #37598

[github-actions]

PR summary 6a7332dd00

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ comp_assoc
+ comp_id
+ id_comp
+ refl_trans
+ trans_assoc
+ trans_refl

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./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).

[SnirBroshi]

Thanks :)

[SnirBroshi]

simp?

Suggested change

	theorem comp_id (f : r →r s) : f.comp (RelHom.id r) = f := rfl
	theorem id_comp (f : r →r s) : (RelHom.id s).comp f = f := rfl
	@[simp]
	theorem comp_id (f : r →r s) : f.comp (RelHom.id r) = f := rfl
	@[simp]
	theorem id_comp (f : r →r s) : (RelHom.id s).comp f = f := rfl

[SnirBroshi]

simp?

Suggested change

	theorem trans_refl (f : r ↪r s) : f.trans (.refl s) = f := rfl
	theorem refl_trans (f : r ↪r s) : .trans (.refl r) f = f := rfl
	@[simp]
	theorem trans_refl (f : r ↪r s) : f.trans (.refl s) = f := rfl
	@[simp]
	theorem refl_trans (f : r ↪r s) : .trans (.refl r) f = f := rfl