Theorems · Theorem · group theory
MulHom.eqOn_closure
∀ {M : Type u_1} {N : Type u_2} [inst : Mul M] [inst_1 : Mul N] {f g : M →ₙ* N} {s : Set M},
Set.EqOn (⇑f) (⇑g) s → Set.EqOn ⇑f ⇑g ↑(Subsemigroup.closure s)If two mul homomorphisms are equal on a set, then they are equal on its subsemigroup closure.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SetLike.coestatement · cited by 8,199
- Set.EqOnstatement and proof · cited by 603
- Subsemigroupstatement · cited by 323
- MulHomstatement and proof · cited by 299
- Subsemigroup.closurestatement and proof · cited by 43
- Subsemigroup.closure_leproof · cited by 13
- MulHom.eqLocusproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MulHom.eq_of_eqOn_denseproof · cited by 0