Theorems · Definition · group theory

Monoid.PushoutI.NormalWord.Transversal.set

{ι : Type u_1} →
  {G : ι → Type u_2} →
    {H : Type u_3} →
      [inst : (i : ι) → Group (G i)] →
        [inst_1 : Group H] → {φ : (i : ι) → H →* G i} → Monoid.PushoutI.NormalWord.Transversal φ → (i : ι) → Set (G i)

The underlying set, containing exactly one element of each coset of the base group

Defined in: Mathlib.GroupTheory.PushoutI
Cited by: 20 results in Mathlib
Foundations: Depth 7 from the axioms · uses no axioms
Assumes: Group Group

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Cites4

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

Setstatement · cited by 53,352
Groupstatement and proof · cited by 6,238
MonoidHomstatement and proof · cited by 3,629
Monoid.PushoutI.NormalWord.Transversalstatement and proof · cited by 45

Cited by31

Results whose statement or proof uses this declaration.

Monoid.PushoutI.NormalWord.Transversal.complstatement · cited by 7
Monoid.PushoutI.NormalWord.Pair.normalizedstatement · cited by 5
Monoid.PushoutI.NormalWord.mk.congr_simpstatement and proof · cited by 4
Monoid.PushoutI.NormalWord.normalizedstatement · cited by 3
Monoid.PushoutI.NormalWord.casesOnstatement and proof · cited by 2
Monoid.PushoutI.NormalWord.Pair.mk.congr_simpstatement and proof · cited by 2
Monoid.PushoutI.NormalWord.consRecOnstatement and proof · cited by 1
Monoid.PushoutI.NormalWord.cons_toListstatement · cited by 1
Monoid.PushoutI.NormalWord.eq_one_of_smul_normalizedstatement and proof · cited by 1
Monoid.PushoutI.NormalWord.extproof · cited by 1
Monoid.PushoutI.NormalWord.ext_smulproof · cited by 1
Monoid.PushoutI.NormalWord.Pair.mk.injstatement and proof · cited by 1