feat(Data/Set): add mono of right inv

[emlis42]

This PR adds some theorems about monotonicity of right inverse of some map.

This is mainly for discoverability and includes a strict version of monotoneOn_of_rightInvOn_of_mapsTo i.e strictMonoOn_of_rightInvOn_of_mapsTo.

Discussed here: Lemmas about StrictMono/Monotone maps with right inverse

[github-actions]

PR summary 5488292cff

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ antitone_of_rightInverse
+ monotone_of_rightInverse
+ strictAntiOn_of_rightInvOn_of_mapsTo
+ strictAnti_of_rightInverse
+ strictMonoOn_of_rightInvOn_of_mapsTo
+ strictMono_of_rightInverse

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.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 5488292).

• +6 new declarations
• −0 removed declarations

+Function.antitone_of_rightInverse
+Function.monotone_of_rightInverse
+Function.strictAntiOn_of_rightInvOn_of_mapsTo
+Function.strictAnti_of_rightInverse
+Function.strictMonoOn_of_rightInvOn_of_mapsTo
+Function.strictMono_of_rightInverse

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 5488292cff
Reference commit d3716e6d2e

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).