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Theorems · Theorem · group theory

AddGroup.rank_congr

∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] [inst_2 : AddGroup.FG G]
  [inst_3 : AddGroup.FG H] (e : G ≃+ H), AddGroup.rank G = AddGroup.rank H
Defined in
Mathlib.GroupTheory.Rank
Cited by
1 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddGroupAddGroup.FGAddGroup.FG
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Around this declaration

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

AddCommGroup.freeRank_congr · cited by 0AddCommGroup.freeRank_con…AddGroup · cited by 4410AddGrouple_antisymm · cited by 2068le_antisymmAddEquiv · cited by 1087AddEquivAddEquiv.symm · cited by 530AddEquiv.symmAddMonoidHomClass.toAddMonoidHom · cited by 232AddMonoidHomClass.toAddMo…AddEquiv.surjective · cited by 37AddEquiv.surjectiveAddGroup.FG · cited by 37AddGroup.FGAddGroup.rank · cited by 14AddGroup.rankAddGroup.rank_le_of_surjective · cited by 3AddGroup.rank_le_of_surje…AddGroup.rank_congrCITED BYCITES

Cites9

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Cited by1

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