Theorems · Definition · group theory
Monoid.CoprodI.Word.cons
{ι : Type u_1} →
{M : ι → Type u_2} →
[inst : (i : ι) → Monoid (M i)] →
{i : ι} → (m : M i) → (w : Monoid.CoprodI.Word M) → w.fstIdx ≠ some i → m ≠ 1 → Monoid.CoprodI.Word MConstruct a new Word without any reduction. The underlying list of
cons m w _ _ is ⟨_, m⟩::w
- Defined in
- Mathlib.GroupTheory.CoprodI
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Monoid.CoprodI.Wordstatement and proof · cited by 55
- Monoid.CoprodI.Word.toListproof · cited by 39
- Monoid.CoprodI.Word.fstIdxstatement and proof · cited by 30
Cited by16
Results whose statement or proof uses this declaration.
- Monoid.CoprodI.Word.rconsproof · cited by 10
- Monoid.PushoutI.NormalWord.consproof · cited by 7
- Monoid.CoprodI.Word.consRecOnstatement and proof · cited by 6
- Monoid.CoprodI.Word.prod_consstatement · cited by 2
- Monoid.CoprodI.Word.cons_eq_smulstatement and proof · cited by 2
- Monoid.CoprodI.Word.cons_toListstatement and proof · cited by 2
- Monoid.CoprodI.Word.equivPair_headproof · cited by 2
- Monoid.CoprodI.Word.mem_equivPair_tail_iffproof · cited by 2
- Monoid.PushoutI.NormalWord.consRecOnproof · cited by 1
- Monoid.PushoutI.NormalWord.cons_eq_smulproof · cited by 1
- Monoid.PushoutI.Reduced.exists_normalWord_prod_eqproof · cited by 1
- Monoid.CoprodI.Word.rcons_injproof · cited by 0