Theorems · Theorem · linear algebra

Module.finrank_bot_le_finrank_of_isScalarTower

∀ (R : Type u) [inst : Semiring R] [StrongRankCondition R] (S : Type u_2) (T : Type u_3) [inst_2 : Semiring S]
  [inst_3 : Semiring T] [inst_4 : Module R T] [inst_5 : Module S T] [inst_6 : Module R S] [IsScalarTower R S T]
  [IsScalarTower S T T] [FaithfulSMul S T] [Module.Finite R T], Module.finrank R S ≤ Module.finrank R T

Also see Module.finrank_bot_le_finrank_of_isScalarTower_of_free for a version with different typeclass constraints.

Defined in: Mathlib.LinearAlgebra.Dimension.StrongRankCondition
Cited by: 1 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring StrongRankCondition Semiring Semiring Module Module Module IsScalarTower IsScalarTower FaithfulSMul Module.Finite

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Cites10

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
Semiringstatement and proof · cited by 13,802
IsScalarTowerstatement and proof · cited by 3,896
Module.finrankstatement · cited by 1,770
Module.Finitestatement and proof · cited by 1,032
FaithfulSMulstatement and proof · cited by 340
StrongRankConditionstatement and proof · cited by 286
Module.rank_lt_aleph0proof · cited by 23
Module.finrank_le_finrank_of_rank_le_rankproof · cited by 7
Module.lift_rank_bot_le_lift_rank_of_isScalarTowerproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Module.finrank_bot_le_finrank_of_isScalarTower_of_freeproof · cited by 0