Theorems · Theorem · group theory
Set.isAddUnit_iff
∀ {α : Type u_2} [inst : SubtractionMonoid α] {s : Set α}, IsAddUnit s ↔ ∃ a, s = {a} ∧ IsAddUnit a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SubtractionMonoid
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.
- Setstatement and proof · cited by 53,352
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
- IsAddUnitstatement and proof · cited by 215
- SubtractionMonoidstatement and proof · cited by 208
- AddUnits.add_negproof · cited by 19
- Set.addMonoidstatement · cited by 18
- AddUnits.neg_addproof · cited by 17
- Set.singleton_injectiveproof · cited by 9
- Set.singleton_add_singletonproof · cited by 3
- Set.add_eq_zero_iffproof · cited by 3
- IsAddUnit.setproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Set.isAddUnit_iff_singletonproof · cited by 0
- Finset.isAddUnit_coeproof · cited by 0