Theorems · Theorem · linear algebra

PiTensorProduct.dualDistribInvOfBasis.congr_simp

∀ {ι : Type u_1} {R : Type u_2} {κ : ι → Type u_3} {M : ι → Type u_4} [inst : CommRing R]
  [inst_1 : (i : ι) → AddCommGroup (M i)] [inst_2 : (i : ι) → Module R (M i)] [inst_3 : Finite ι]
  [inst_4 : ∀ (i : ι), Finite (κ i)] (b b_1 : (i : ι) → Module.Basis (κ i) R (M i)),
  b = b_1 → PiTensorProduct.dualDistribInvOfBasis b = PiTensorProduct.dualDistribInvOfBasis b_1

Defined in: Mathlib.LinearAlgebra.PiTensorProduct.Dual
Cited by: 0 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Finite Finite

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Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Finitestatement and proof · cited by 3,029
Module.Basisstatement and proof · cited by 1,477
Module.Dualstatement · cited by 583
PiTensorProductstatement · cited by 181
PiTensorProduct.dualDistribInvOfBasisstatement and proof · cited by 5

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