Theorems · Theorem · group theory
Monoid.CoprodI.NeWord.of_word
∀ {ι : Type u_1} {M : ι → Type u_2} [inst : (i : ι) → Monoid (M i)] (w : Monoid.CoprodI.Word M),
w ≠ Monoid.CoprodI.Word.empty → ∃ i j w', w'.toWord = wEvery nonempty Word M can be constructed as a NeWord M i j
- Defined in
- Mathlib.GroupTheory.CoprodI
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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.
Cites14
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.NeWordstatement and proof · cited by 36
- Sigma.etaproof · cited by 25
- Monoid.CoprodI.Word.emptystatement and proof · cited by 12
- Monoid.CoprodI.NeWord.headproof · cited by 12
- Monoid.CoprodI.NeWord.toListproof · cited by 7
- Monoid.CoprodI.Word.extproof · cited by 4
- Monoid.CoprodI.Word.casesOnproof · cited by 3
- Monoid.CoprodI.Word.mk.congr_simpproof · cited by 3
- Monoid.CoprodI.NeWord.toWordstatement and proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.CoprodI.empty_of_word_prod_eq_oneproof · cited by 1