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feat(LinearAlgebra/Alternating): add map_eq_zero_of_card_lt #34052

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feat(LinearAlgebra/Alternating): add map_eq_zero_of_card_lt #34052

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5 changes: 5 additions & 0 deletions Mathlib/LinearAlgebra/Alternating/Basic.lean
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Expand Up @@ -10,6 +10,7 @@ public import Mathlib.LinearAlgebra.LinearIndependent.Defs
public import Mathlib.LinearAlgebra.Multilinear.Basis

import Mathlib.Algebra.Module.Torsion.Pi
import Mathlib.Data.Fintype.Pigeonhole

/-!
# Alternating Maps
Expand Down Expand Up @@ -195,6 +196,10 @@ theorem map_eq_zero_of_not_injective (v : ι → M) (hv : ¬Function.Injective v
rcases hv with ⟨i₁, i₂, heq, hne⟩
exact f.map_eq_zero_of_eq v heq hne

theorem map_eq_zero_of_card_lt [Fintype ι] [Fintype M] (v : ι → M)
(h : Fintype.card M < Fintype.card ι) : f v = 0 := by
obtain ⟨i, j, hne, heq⟩ := Fintype.exists_ne_map_eq_of_card_lt v h
exact f.map_eq_zero_of_eq v heq hne
/-!
### Algebraic structure inherited from `MultilinearMap`

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