Theorems · Theorem · linear algebra

AlternatingMap.map_swap_add

∀ {R : Type u_1} [inst : Semiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Type u_3}
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] {ι : Type u_7} (f : M [⋀^ι]→ₗ[R] N) (v : ι → M)
  [inst_5 : DecidableEq ι] {i j : ι}, i ≠ j → f (v ∘ ⇑(Equiv.swap i j)) + f v = 0

Defined in

Mathlib.LinearAlgebra.Alternating.Basic

Cited by

2 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEq