Theorems · Theorem · linear algebra

TensorProduct.dualDistribInvOfBasis.congr_simp

∀ {R : Type u_7} {M : Type u_8} {N : Type u_9} {ι : Type u_10} {κ : Type u_11} {inst : DecidableEq ι}
  [inst_1 : DecidableEq ι] {inst_2 : DecidableEq κ} [inst_3 : DecidableEq κ] [inst_4 : Fintype ι] [inst_5 : Fintype κ]
  [inst_6 : CommSemiring R] [inst_7 : AddCommMonoid M] [inst_8 : AddCommMonoid N] [inst_9 : Module R M]
  [inst_10 : Module R N] (b b_1 : Module.Basis ι R M),
  b = b_1 →
    ∀ (c c_1 : Module.Basis κ R N),
      c = c_1 → TensorProduct.dualDistribInvOfBasis b c = TensorProduct.dualDistribInvOfBasis b_1 c_1

Defined in

Mathlib.LinearAlgebra.Contraction

Cited by

0 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqDecidableEqFintypeFintypeCommSemiringAddCommMonoidAddCommMonoidModuleModule