Theorems · Theorem · linear algebra

Finsupp.lcongr_single

∀ {M : Type u_2} {N : Type u_3} {R : Type u_5} {R₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : AddCommMonoid N] [inst_5 : Module R₂ N] {σ : R →+* R₂}
  {σ_inv : R₂ →+* R} [inst_6 : RingHomInvPair σ σ_inv] [inst_7 : RingHomInvPair σ_inv σ] {ι : Type u_9} {κ : Type u_10}
  (e₁ : ι ≃ κ) (e₂ : M ≃ₛₗ[σ] N) (i : ι) (m : M), ((Finsupp.lcongr e₁ e₂) fun₀ | i => m) = fun₀ | e₁ i => e₂ m

Defined in

Mathlib.LinearAlgebra.Finsupp.LSum

Cited by

12 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleAddCommMonoidModuleRingHomInvPairRingHomInvPair