Theorems · Theorem · group theory
IsAddUnit.preimage_vadd_set
∀ {M : Type u_1} {α : Type u_2} {β : Type u_3} {F : Type u_4} [inst : AddMonoid M] [inst_1 : AddAction M α]
[inst_2 : AddAction M β] [inst_3 : FunLike F α β] [AddActionHomClass F M α β] (f : F) {c : M},
IsAddUnit c → ∀ (t : Set β), ⇑f ⁻¹' (c +ᵥ t) = c +ᵥ ⇑f ⁻¹' t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.preimagestatement · cited by 4,946
- AddMonoidstatement and proof · cited by 2,864
- FunLikestatement and proof · cited by 2,560
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- IsAddUnitstatement and proof · cited by 215
- AddActionHomClassstatement and proof · cited by 9
- preimage_vadd_setₛₗ_of_isAddUnit_isAddUnitproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddGroup.preimage_vadd_setproof · cited by 0