Theorems · Theorem · commutative algebra
Ideal.Quotient.mk_eq_one_iff_sub_mem
∀ {R : Type u} [inst : Ring R] {I : Ideal R} [inst_1 : I.IsTwoSided] (x : R), (Ideal.Quotient.mk I) x = 1 ↔ x - 1 ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- map_oneproof · cited by 861
- Ideal.Quotient.mkstatement and proof · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.Quotient.mk_eq_mk_iff_sub_memproof · cited by 8
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