Theorems · Definition · group theory
QuotientAddGroup.mk
{α : Type u_1} → [inst : AddGroup α] → {s : AddSubgroup α} → α → α ⧸ sThe canonical map from an AddGroup α to the quotient α ⧸ s.
- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 348 results in Mathlib
- Foundations
- Depth 68 from the axioms, rests on 832 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- Quotient.mk''proof · cited by 132
Cited by371
Results whose statement or proof uses this declaration.
- Real.Angle.coeproof · cited by 360
- QuotientAddGroup.mk'proof · cited by 60
- QuotientAddGroup.induction_onstatement and proof · cited by 33
- ZMod.toAddCircleproof · cited by 32
- QuotientAddGroup.eqstatement · cited by 24
- QuotientAddGroup.eq_zero_iffstatement · cited by 19
- Orientation.oangle_selfproof · cited by 17
- QuotientAddGroup.mk_surjectivestatement · cited by 11
- QuotientAddGroup.mk_zerostatement · cited by 10
- AddSubgroup.IsComplement.leftQuotientEquivproof · cited by 8
- Real.Angle.angle_eq_iff_two_pi_dvd_subproof · cited by 8
- fourier_coe_applystatement and proof · cited by 7
Showing the 200 most cited of 371.