Theorems · Theorem · linear algebra

iSupIndep.subtype_ne_bot_le_rank

∀ {ι : Type w} {R : Type u} {M : Type v} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsDomain R]
  [Module.IsTorsionFree R M] {V : ι → Submodule R M},
  iSupIndep V → Cardinal.lift.{v, w} (Cardinal.mk { i // V i ≠ ⊥ }) ≤ Cardinal.lift.{w, v} (Module.rank R M)

Defined in: Mathlib.LinearAlgebra.Dimension.Finite
Cited by: 1 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module IsDomain Module.IsTorsionFree

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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
Ringstatement and proof · cited by 7,463
Submodulestatement and proof · cited by 7,192
Bot.botstatement and proof · cited by 4,720
Cardinalstatement · cited by 2,598
IsDomainstatement and proof · cited by 2,196
Cardinal.mkstatement and proof · cited by 942
Module.IsTorsionFreestatement and proof · cited by 600
Cardinal.liftstatement and proof · cited by 583
LinearIndependentproof · cited by 560
Subtype.propproof · cited by 505

Cited by1

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iSupIndep.subtype_ne_bot_le_finrank_auxproof · cited by 1