Theorems · Theorem · group theory
FreeSemigroup.toFreeMonoid_mk_eq_cons
∀ {α : Type u_1} (x : α) (xs : List α),
FreeSemigroup.toFreeMonoid { head := x, tail := xs } = FreeMonoid.ofList (x :: xs)- Defined in
- Mathlib.Algebra.FreeMonoid.FreeSemigroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- MulHomstatement and proof · cited by 299
- FreeMonoidstatement and proof · cited by 147
- FreeMonoid.ofproof · cited by 69
- Equiv.mk.congr_simpproof · cited by 54
- FreeSemigroupstatement and proof · cited by 43
- FreeMonoid.ofListstatement and proof · cited by 26
- FreeSemigroup.ofproof · cited by 20
- FreeSemigroup.toFreeMonoidstatement · cited by 7
- FreeSemigroup.headproof · cited by 6
- FreeSemigroup.tailproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- FreeSemigroup.toFreeMonoid_injectiveproof · cited by 0