Theorems · Theorem · linear algebra

Module.finrank_top_le_finrank_of_isScalarTower_of_free

∀ (R : Type u) (S : Type u_1) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [StrongRankCondition R] [inst_4 : Semiring S] [StrongRankCondition S] [inst_6 : Module S M] [inst_7 : Module R S]
  [FaithfulSMul R S] [Module.Finite R S] [IsScalarTower R S S] [IsScalarTower R S M] [Module.Free S M],
  Module.finrank S M ≤ Module.finrank R M

Also see Module.finrank_top_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 AddCommMonoid Module StrongRankCondition Semiring StrongRankCondition Module Module FaithfulSMul Module.Finite IsScalarTower IsScalarTower Module.Free

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Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
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

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