Theorems · Definition · group theory

AddSubgroup.quotientiInfAddSubgroupOfEmbedding

{α : Type u_1} →
  [inst : AddGroup α] →
    {ι : Type u_2} →
      (f : ι → AddSubgroup α) →
        (H : AddSubgroup α) → ↥H ⧸ (⨅ i, f i).addSubgroupOf H ↪ (i : ι) → ↥H ⧸ (f i).addSubgroupOf H

The natural embedding H ⧸ (⨅ i, f i).addSubgroupOf H) ↪ Π i, H ⧸ (f i).addSubgroupOf H.

Defined in: Mathlib.GroupTheory.Coset.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup

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Cites7

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

AddGroupstatement and proof · cited by 4,410
AddSubgroupstatement and proof · cited by 3,232
HasQuotient.Quotientstatement and proof · cited by 2,301
iInfstatement and proof · cited by 1,690
Function.Embeddingstatement · cited by 988
AddSubgroup.addSubgroupOfstatement and proof · cited by 87
AddSubgroup.quotientAddSubgroupOfMapOfLEproof · cited by 2

Cited by4

Results whose statement or proof uses this declaration.

AddSubgroup.relIndex_iInf_leproof · cited by 1
AddSubgroup.relIndex_iInf_ne_zeroproof · cited by 1
AddSubgroup.quotientiInfAddSubgroupOfEmbedding_applystatement and proof · cited by 0
AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply_mkstatement · cited by 0