Theorems · Theorem · group theory
AddSubgroup.index_bot
∀ {G : Type u_1} [inst : AddGroup G], ⊥.index = Nat.card G- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Nat.cardstatement · cited by 844
- AddEquiv.toEquivproof · cited by 174
- Nat.card_congrproof · cited by 133
- AddSubgroup.indexstatement · cited by 104
- QuotientAddGroup.quotientBotproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.card_mul_indexproof · cited by 7
- AddSubgroup.relIndex_bot_leftproof · cited by 4
- Module.Basis.SmithNormalForm.toAddSubgroup_index_eq_pow_mul_prodproof · cited by 1
- Submodule.cardQuot_botproof · cited by 1