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Theorems · Theorem · group theory

IsAddKleinFour.nonempty_addEquiv

∀ {G₁ : Type u_2} {G₂ : Type u_3} [inst : AddGroup G₁] [inst_1 : AddGroup G₂] [IsAddKleinFour G₁] [IsAddKleinFour G₂],
  Nonempty (G₁ ≃+ G₂)

Any two IsAddKleinFour groups are isomorphic.

Defined in
Mathlib.GroupTheory.SpecificGroups.KleinFour
Cited by
0 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddGroupIsAddKleinFourIsAddKleinFour
Mathlib docsSourceLoogleLeanSearch

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Fintype · cited by 7736FintypeAddGroup · cited by 4410AddGroupAddEquiv · cited by 1087AddEquivFintype.ofFinite · cited by 255Fintype.ofFiniteFintype.equivOfCardEq · cited by 23Fintype.equivOfCardEqIsAddKleinFour · cited by 10IsAddKleinFourEquiv.setValue · cited by 3Equiv.setValueIsAddKleinFour.card_four' · cited by 2IsAddKleinFour.card_four'Equiv.setValue_eq · cited by 2Equiv.setValue_eqIsAddKleinFour.addEquiv · cited by 1IsAddKleinFour.addEquivIsAddKleinFour.nonempty_addEq…CITED BYCITES

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