Theorems · Theorem · group theory
Subsemigroup.map_iInf
∀ {M : Type u_1} {N : Type u_2} [inst : Mul M] [inst_1 : Mul N] {ι : Sort u_5} [Nonempty ι] (f : M →ₙ* N),
Function.Injective ⇑f → ∀ (s : ι → Subsemigroup M), Subsemigroup.map f (iInf s) = ⨅ i, Subsemigroup.map f (s i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Set.imageproof · cited by 5,609
- iInfstatement and proof · cited by 1,690
- SetLike.coe_injectiveproof · cited by 374
- Subsemigroupstatement and proof · cited by 323
- MulHomstatement and proof · cited by 299
- Subsemigroup.mapstatement and proof · cited by 51
- Set.injOn_of_injectiveproof · cited by 28
- Set.InjOn.image_iInter_eqproof · cited by 22
- Subsemigroup.coe_iInfproof · cited by 1
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