feat(LinearAlgebra): rank-nullity theorems for Submodule map/comap

[ChiCubed]

We show forms of the rank-nullity theorem involving Submodule.map and Submodule.comap. Together with LinearMap.ker_comp this provides a formula for the rank of the kernel of a composite (and, in finite dimensions at least, for the rank of the range).

---

I didn't explicitly write the aforementioned formula for rank ker (f ∘ g) since it is just LinearMap.ker_comp followed by LinearMap.lift_rank_comap, but perhaps it should be added for discoverability?

[github-actions]

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[github-actions]

PR summary 13c9652f88

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ LinearMap.lift_rank_comap
+ LinearMap.lift_rank_map_add_rank_ker_inf
+ LinearMap.rank_comap
+ LinearMap.rank_map_add_rank_ker_inf
+ ker_submoduleComap
+ ker_submoduleMap
+ map_subtype_submoduleOf
+ range_submoduleComap
+ range_submoduleMap
+ submoduleOfEquivInf

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 13c9652).

• +10 new declarations
• −0 removed declarations

+LinearMap.ker_submoduleComap
+LinearMap.ker_submoduleMap
+LinearMap.lift_rank_comap
+LinearMap.lift_rank_map_add_rank_ker_inf
+LinearMap.range_submoduleComap
+LinearMap.range_submoduleMap
+LinearMap.rank_comap
+LinearMap.rank_map_add_rank_ker_inf
+Submodule.map_subtype_submoduleOf
+Submodule.submoduleOfEquivInf

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 13c9652f88
Reference commit 4fcc8d62a4

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).

[wwylele]

This one doesn't need (_ :)

Suggested change

	map q.subtype (p.submoduleOf q) = (p ⊓ q :) := by
	map q.subtype (p.submoduleOf q) = p ⊓ q := by