Theorems · Theorem · group theory
IsKleinFour.eq_finset_univ
∀ {G : Type u_1} [inst : Group G] [IsKleinFour G] [inst_2 : Fintype G] [inst_3 : DecidableEq G] {x y : G},
x ≠ 1 → y ≠ 1 → x ≠ y → {x * y, x, y, 1} = Finset.univ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 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.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Finset.univstatement · cited by 3,473
- Finset.cardproof · cited by 2,327
- Finset.card_singletonproof · cited by 144
- Finset.card_insert_of_notMemproof · cited by 45
- IsKleinFourstatement and proof · cited by 11
- Finset.eq_univ_of_cardproof · cited by 5
- IsKleinFour.exponent_twoproof · cited by 4
- IsKleinFour.card_four'proof · cited by 2
- mul_notMem_of_exponent_twoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsKleinFour.eq_mul_of_ne_allproof · cited by 0