Theorems · Definition · group theory

Monoid.PushoutI.NormalWord.prod

{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} →
            {d : Monoid.PushoutI.NormalWord.Transversal φ} → Monoid.PushoutI.NormalWord d → Monoid.PushoutI φ

Take the product of a normal word as an element of the PushoutI. We show that this is bijective, in NormalWord.equiv.

Defined in

Mathlib.GroupTheory.PushoutI

Cited by

9 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Quot.sound

Assumes

GroupGroup