Theorems · Theorem · linear algebra

Submodule.comap_finsetInf

∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}
  {ι : Type u_9} (f : M →ₛₗ[σ₁₂] M₂) (s : Finset ι) (p : ι → Submodule R₂ M₂),
  Submodule.comap f (s.inf p) = s.inf fun i => Submodule.comap f (p i)

Defined in: Mathlib.Algebra.Module.Submodule.Map
Cited by: 1 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring Semiring AddCommMonoid AddCommMonoid Module Module

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Cites12

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
Semiringstatement and proof · cited by 13,802
Finsetstatement and proof · cited by 13,712
AddCommMonoidstatement and proof · cited by 12,281
LinearMapstatement and proof · cited by 10,215
RingHomstatement and proof · cited by 10,189
Submodulestatement and proof · cited by 7,192
iInfproof · cited by 1,690
Submodule.comapstatement and proof · cited by 347
Finset.infstatement · cited by 219
Finset.inf_eq_iInfproof · cited by 19
Submodule.comap_iInfproof · cited by 7

Cited by1

Results whose statement or proof uses this declaration.

Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_iInfproof · cited by 0