Theorems · Theorem · linear algebra

FiniteDimensional.trans

∀ (F : Type u_1) (K : Type u_2) (A : Type u_3) [inst : DivisionRing F] [inst_1 : DivisionRing K]
  [inst_2 : AddCommGroup A] [inst_3 : Module F K] [inst_4 : Module K A] [inst_5 : Module F A] [IsScalarTower F K A]
  [FiniteDimensional F K] [FiniteDimensional K A], FiniteDimensional F A

Defined in: Mathlib.LinearAlgebra.FiniteDimensional.Defs
Cited by: 3 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing DivisionRing AddCommGroup Module Module Module IsScalarTower FiniteDimensional FiniteDimensional

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
IsScalarTowerstatement and proof · cited by 3,896
FiniteDimensionalstatement and proof · cited by 1,854
DivisionRingstatement and proof · cited by 1,062
Module.Finite.transproof · cited by 16

Cited by3

Results whose statement or proof uses this declaration.

FiniteDimensional.proper_rclikeproof · cited by 3
IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
FunctionField.finiteDimensional_of_adjoin_transcendentalproof · cited by 0