Mathlib Map

Theorems · Inductive type · group theory

IsAddKleinFour

(G : Type u_1) → [AddGroup G] → Prop

An (additive) Klein four-group is an (additive) group of cardinality four and exponent two.

Defined in
Mathlib.GroupTheory.SpecificGroups.KleinFour
Cited by
10 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsAddKleinFour.exponent_two · cited by 4IsAddKleinFour.exponent_t…IsAddKleinFour.card_four · cited by 2IsAddKleinFour.card_fourIsAddKleinFour.card_four' · cited by 2IsAddKleinFour.card_four'IsAddKleinFour.neg_eq_self · cited by 1IsAddKleinFour.neg_eq_selfIsAddKleinFour.addEquiv · cited by 1IsAddKleinFour.addEquivIsAddKleinFour.eq_finset_univ · cited by 1IsAddKleinFour.eq_finset_…IsAddKleinFour.nonempty_addEquiv · cited by 0IsAddKleinFour.nonempty_a…IsAddKleinFour.not_isAddCyclic · cited by 0IsAddKleinFour.not_isAddC…IsAddKleinFour.recOn · cited by 0IsAddKleinFour.recOnIsAddKleinFour.addEquiv' · cited by 0IsAddKleinFour.addEquiv'IsAddKleinFour.add_self · cited by 0IsAddKleinFour.add_selfIsAddKleinFour.casesOn · cited by 0IsAddKleinFour.casesOnIsAddKleinFour.eq_add_of_ne_all · cited by 0IsAddKleinFour.eq_add_of_…IsAddKleinFour.isAddCommutative · cited by 0IsAddKleinFour.isAddCommu…AddGroup · cited by 4410AddGroupIsAddKleinFourCITED BYCITES

Cites1

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by14

Results whose statement or proof uses this declaration.