Theorems · Theorem · linear algebra

Module.finrank_bot_le_finrank_of_isScalarTower_of_free

∀ (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 S T] [Module.Free R S],
  Module.finrank R S ≤ Module.finrank R T

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

Defined in: Mathlib.LinearAlgebra.Dimension.Free
Cited by: 0 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring StrongRankCondition Semiring Semiring Module Module Module IsScalarTower IsScalarTower FaithfulSMul Module.Finite Module.Free

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Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
IsScalarTowerstatement and proof · cited by 3,896
Module.finrankstatement and proof · cited by 1,770
Module.Finitestatement and proof · cited by 1,032
Module.Freestatement and proof · cited by 597
zero_leproof · cited by 382
FaithfulSMulstatement and proof · cited by 340
not_ltproof · cited by 306
StrongRankConditionstatement and proof · cited by 286
Module.Finite.transproof · cited by 16
Module.rank_lt_aleph0_iffproof · cited by 8

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