Theorems · Theorem · group theory
IsAddKleinFour.eq_add_of_ne_all
∀ {G : Type u_1} [inst : AddGroup G] [IsAddKleinFour G] {x y z : G},
x ≠ 0 → y ≠ 0 → x ≠ y → z ≠ 0 → z ≠ x → z ≠ y → z = x + y- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupIsAddKleinFour
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- AddGroupstatement and proof · cited by 4,410
- Finset.mem_univproof · cited by 361
- Fintype.ofFiniteproof · cited by 255
- Finset.mem_singletonproof · cited by 103
- Finset.mem_insertproof · cited by 44
- IsAddKleinFourstatement and proof · cited by 10
- Finset.eq_of_mem_insert_of_notMemproof · cited by 4
- IsAddKleinFour.eq_finset_univproof · cited by 1
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