Theorems · Theorem · linear algebra

OrzechProperty.bijective_of_surjective_of_finrank_le

∀ {R : Type u} {M : Type v} {M' : Type v'} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [Module.Free R M] [inst_4 : AddCommMonoid M'] [inst_5 : Module R M'] [Module.Free R M'] [OrzechProperty R]
  [Module.Finite R M] [Module.Finite R M'] (f : M →ₗ[R] M'),
  Function.Surjective ⇑f → Module.finrank R M ≤ Module.finrank R M' → Function.Bijective ⇑f

Defined in: Mathlib.LinearAlgebra.Dimension.Free
Cited by: 1 results in Mathlib
Foundations: Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module Module.Free AddCommMonoid Module Module.Free OrzechProperty Module.Finite Module.Finite

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Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
LinearMapstatement and proof · cited by 10,215
Nontrivialproof · cited by 2,416
Module.finrankstatement and proof · cited by 1,770
Module.Finitestatement and proof · cited by 1,032
Function.Bijectivestatement · cited by 863
Module.Freestatement and proof · cited by 597
subsingleton_or_nontrivialproof · cited by 161

Cited by1

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Module.bijective_of_surjective_of_rankAtStalk_eqproof · cited by 1