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Theorems · Theorem · group theory

Monoid.CoprodI.of_apply

∀ {ι : Type u_1} {M : ι → Type u_2} [inst : (i : ι) → Monoid (M i)] {i : ι} (m : M i),
  Monoid.CoprodI.of m = (conGen (Monoid.CoprodI.Rel M)).mk' (FreeMonoid.of ⟨i, m⟩)
Defined in
Mathlib.GroupTheory.CoprodI
Cited by
1 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Quot.sound
Assumes
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Monoid.CoprodI.ext_hom · cited by 2CoprodI.ext_homDFunLike.coe · cited by 62936DFunLike.coeMonoid · cited by 3887MonoidMonoidHom · cited by 3629MonoidHomFreeMonoid · cited by 147FreeMonoidFreeMonoid.of · cited by 69FreeMonoid.ofMonoid.CoprodI · cited by 52Monoid.CoprodICon.Quotient · cited by 48Con.QuotientMonoid.CoprodI.of · cited by 45CoprodI.ofconGen · cited by 23conGenCon.mk' · cited by 22Con.mk'Monoid.CoprodI.Rel · cited by 3CoprodI.RelCoprodI.of_applyCITED BYCITES

Cites11

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

Cited by1

Results whose statement or proof uses this declaration.