Mathlib Map

Theorems · Theorem · group theory

AddSubgroup.index_top

∀ {G : Type u_1} [inst : AddGroup G], ⊤.index = 1
Defined in
Mathlib.GroupTheory.Index
Cited by
9 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup
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Around this declaration

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

AddSubgroup.relIndex_top_right · cited by 7AddSubgroup.relIndex_top_…AddSubgroup.index_eq_one · cited by 4AddSubgroup.index_eq_oneSubmodule.cardQuot_top · cited by 2Submodule.cardQuot_topAddSubgroup.relIndex_self · cited by 2AddSubgroup.relIndex_selfAddSubgroup.index_dvd_two_iff · cited by 2AddSubgroup.index_dvd_two…AddSubgroup.index_map_dvd · cited by 1AddSubgroup.index_map_dvdIdeal.index_pow_le · cited by 0Ideal.index_pow_leAddSubgroup.relIndex_bot_right · cited by 0AddSubgroup.relIndex_bot_…AddSubgroup.relIndex_top_left · cited by 0AddSubgroup.relIndex_top_…Top.top · cited by 9680Top.topAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddSubgroup.index · cited by 104AddSubgroup.indexNat.card_eq_one_iff_unique · cited by 15Nat.card_eq_one_iff_uniqueQuotientAddGroup.subsingleton_quotient_top · cited by 1QuotientAddGroup.subsingl…AddSubgroup.index_topCITED BYCITES

Cites6

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

Cited by9

Results whose statement or proof uses this declaration.