Theorems · Theorem · commutative algebra
Ideal.Quotient.mk_out
∀ {R : Type u} [inst : Ring R] {I : Ideal R} [inst_1 : I.IsTwoSided] (x : R ⧸ I),
(Ideal.Quotient.mk I) (Quotient.out x) = x- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Quotient.outstatement · cited by 141
- Quotient.out_eqproof · cited by 27
- Submodule.quotientRelstatement · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- Perfection.mk_teichmullerproof · cited by 5
- Perfection.teichmullerFun_sModEqproof · cited by 3
- Perfection.teichmullerAux_sModEqproof · cited by 0
- MvPowerSeries.mk_truncTotal_toAdicCompletionInvproof · cited by 0
- MvPowerSeries.coeff_toAdicCompletion_val_apply_outproof · cited by 0