Theorems · Theorem · group theory
Submonoid.map_iInf
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] {F : Type u_4} [inst_2 : FunLike F M N]
[mc : MonoidHomClass F M N] {ι : Sort u_5} [Nonempty ι] (f : F),
Function.Injective ⇑f → ∀ (s : ι → Submonoid M), Submonoid.map f (iInf s) = ⨅ i, Submonoid.map f (s i)- Cited by
- 0 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.
Cites12
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
- Submonoidstatement and proof · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- iInfstatement and proof · cited by 1,690
- MulOneClassstatement and proof · cited by 1,018
- SetLike.coe_injectiveproof · cited by 374
- MonoidHomClassstatement and proof · cited by 244
- Submonoid.mapstatement and proof · cited by 190
- Set.injOn_of_injectiveproof · cited by 28
- Set.InjOn.image_iInter_eqproof · cited by 22
- Submonoid.coe_iInfproof · cited by 1
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