Theorems · Theorem · linear algebra

Module.finrank_le_finrank_of_rank_le_rank

∀ {R : Type u} {M : Type v} {N : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N],
  Cardinal.lift.{w, v} (Module.rank R M) ≤ Cardinal.lift.{v, w} (Module.rank R N) →
    Module.rank R N < Cardinal.aleph0 → Module.finrank R M ≤ Module.finrank R N

Defined in

Mathlib.LinearAlgebra.Dimension.Finrank

Cited by

7 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModule