Theorems · Theorem · group theory

PresentedGroup.lift_toCoprod_eq_one

∀ {α : Type u_1} {β : Type u_2} (rels₁ : Set (FreeGroup α)) (rels₂ : Set (FreeGroup β)),
  ∀ r ∈ ⇑(FreeGroup.map Sum.inl) '' rels₁ ∪ ⇑(FreeGroup.map Sum.inr) '' rels₂,
    (FreeGroup.lift (PresentedGroup.toCoprod rels₁ rels₂)) r = 1

Defined in

Mathlib.GroupTheory.PresentedGroup

Cited by

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Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound