Theorems · Theorem · ring theory
TwoSidedIdeal.mem_sup
∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] {I J : TwoSidedIdeal R} {x : R},
x ∈ I ⊔ J ↔ ∃ y ∈ I, ∃ z ∈ J, y + z = x- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalNonAssocRing
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.ofPredproof · cited by 6,101
- add_zeroproof · cited by 2,707
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- mul_addproof · cited by 413
- add_mulproof · cited by 363
- NonUnitalNonAssocRingstatement and proof · cited by 354
- sup_leproof · cited by 159
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConproof · cited by 40
- TwoSidedIdeal.mk'proof · cited by 8
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