Theorems · Theorem · group theory
MonoidHom.eq_of_eqOn_denseM
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] {s : Set M},
Submonoid.closure s = ⊤ → ∀ {f g : M →* N}, Set.EqOn (⇑f) (⇑g) s → f = g- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClassMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- MonoidHomstatement and proof · cited by 3,629
- Submonoidstatement · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Set.EqOnstatement and proof · cited by 603
- Submonoid.closurestatement and proof · cited by 167
- MonoidHom.eqOn_closureMproof · cited by 1
- MonoidHom.eq_of_eqOn_topMproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Monoid.Coprod.hom_extproof · cited by 14
- PresentedMonoid.extproof · cited by 1
- CoxeterSystem.ext_simpleproof · cited by 1