Theorems · Theorem · linear algebra

Module.Basis.equiv_apply

∀ {ι' : Type u_2} {M' : Type u_7} [inst : AddCommMonoid M'] {ι : Type u_10} {R : Type u_11} {M : Type u_12}
  [inst_1 : Semiring R] [inst_2 : AddCommMonoid M] [inst_3 : Module R M] (b : Module.Basis ι R M) [inst_4 : Module R M']
  (i : ι) (b' : Module.Basis ι' R M') (e : ι ≃ ι'), (b.equiv b' e) (b i) = b' (e i)

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

13 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidSemiringAddCommMonoidModuleModule