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Theorems · Theorem · group theory

QuotientAddGroup.induction_on

∀ {α : Type u_1} [inst : AddGroup α] {s : AddSubgroup α} {C : α ⧸ s → Prop} (x : α ⧸ s), (∀ (z : α), C ↑z) → C x
Defined in
Mathlib.GroupTheory.Coset.Defs
Cited by
33 results in Mathlib
Foundations
Depth 69 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.

QuotientAddGroup.addMonoidHom_ext · cited by 6QuotientAddGroup.addMonoi…AddCircle.injective_toCircle · cited by 4AddCircle.injective_toCir…AddCircle.toCircle_add · cited by 4AddCircle.toCircle_addfourier_neg · cited by 3fourier_negHurwitzZeta.oddKernel_neg · cited by 2HurwitzZeta.oddKernel_negAddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHom · cited by 2AddCommGroup.isAddTorsion…HurwitzZeta.sinKernel_neg · cited by 2HurwitzZeta.sinKernel_negAddCircle.homeomorphCircle_apply · cited by 2AddCircle.homeomorphCircl…AddCircle.addOrderOf_eq_pos_iff · cited by 2AddCircle.addOrderOf_eq_p…QuotientAddGroup.orbit_eq_out_vadd · cited by 1QuotientAddGroup.orbit_eq…HurwitzZeta.oddKernel_undef · cited by 1HurwitzZeta.oddKernel_und…HurwitzZeta.sinKernel_undef · cited by 1HurwitzZeta.sinKernel_und…HurwitzZeta.cosKernel_neg · cited by 1HurwitzZeta.cosKernel_negHurwitzZeta.cosKernel_undef · cited by 1HurwitzZeta.cosKernel_und…HurwitzZeta.evenKernel_neg · cited by 1HurwitzZeta.evenKernel_negAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupHasQuotient.Quotient · cited by 2301HasQuotient.QuotientQuotientAddGroup.mk · cited by 348QuotientAddGroup.mkQuotient.inductionOn' · cited by 69Quotient.inductionOn'QuotientAddGroup.induction_onCITED BYCITES

Cites5

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Cited by33

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