feat(LinearAlgebra/Alternating): add map_eq_zero_of_card_lt

[JohnnyTeutonic]

Adds a theorem stating that an alternating map is zero on any input when the index type has strictly more elements than the target of the input function (pigeonhole principle).

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[github-actions]

PR summary 2b4c6152f1

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.Alternating.Basic	945	946	+1 (+0.11%)

Import changes for all files

Files

Import difference

20 files Mathlib.Data.Matrix.Cartan Mathlib.LinearAlgebra.Alternating.Basic Mathlib.LinearAlgebra.Alternating.Curry Mathlib.LinearAlgebra.Alternating.DomCoprod Mathlib.LinearAlgebra.Alternating.Uncurry.Fin Mathlib.LinearAlgebra.CrossProduct Mathlib.LinearAlgebra.Matrix.AbsoluteValue Mathlib.LinearAlgebra.Matrix.Basis Mathlib.LinearAlgebra.Matrix.Determinant.Basic Mathlib.LinearAlgebra.Matrix.Determinant.Misc Mathlib.LinearAlgebra.Matrix.Determinant.TotallyUnimodular Mathlib.LinearAlgebra.Matrix.IsDiag Mathlib.LinearAlgebra.Matrix.Kronecker Mathlib.LinearAlgebra.Matrix.MvPolynomial Mathlib.LinearAlgebra.Matrix.Reindex Mathlib.LinearAlgebra.Matrix.Transvection Mathlib.LinearAlgebra.Matrix.Vec Mathlib.LinearAlgebra.TensorProduct.Matrix Mathlib.RingTheory.MatrixAlgebra Mathlib.Topology.Algebra.Module.Alternating.Basic

1

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Declarations diff

+ finrank_ker_traceLinearMap
+ map_eq_zero_of_card_lt

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.

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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).