Theorems · Theorem · group theory
Set.nonempty_inv
∀ {α : Type u_2} [inst : InvolutiveInv α] {s : Set α}, s⁻¹.Nonempty ↔ s.Nonempty- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- InvolutiveInv
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement · cited by 2,627
- Set.invstatement · cited by 132
- InvolutiveInvstatement and proof · cited by 102
- Function.Involutive.surjectiveproof · cited by 23
- inv_involutiveproof · cited by 12
- Function.Surjective.nonempty_preimageproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Set.Nonempty.invproof · cited by 2
- Set.nonempty_image_mulLeft_inv_inter_iffproof · cited by 1
- Set.nonempty_image_mulRight_inv_inter_iffproof · cited by 0