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Theorems · Theorem · ring theory

NonUnitalSubsemiring.ext

∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] {S T : NonUnitalSubsemiring R}, (∀ (x : R), x ∈ S ↔ x ∈ T) → S = T

Two non-unital subsemirings are equal if they have the same elements.

Defined in
Mathlib.RingTheory.NonUnitalSubsemiring.Defs
Cited by
6 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
NonUnitalNonAssocSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subsemigroup.nonUnitalSubsemiringClosure_eq_closure · cited by 2Subsemigroup.nonUnitalSub…NonUnitalRingHom.srange_eq_map · cited by 1NonUnitalRingHom.srange_e…NonUnitalSubsemiring.top_prod · cited by 1NonUnitalSubsemiring.top_…NonUnitalSubsemiring.ext_iff · cited by 0NonUnitalSubsemiring.ext_…NonUnitalSubsemiring.closure_addSubmonoid_closure · cited by 0NonUnitalSubsemiring.clos…NonUnitalSubsemiring.prod_top · cited by 0NonUnitalSubsemiring.prod…NonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringSetLike.ext · cited by 92SetLike.extNonUnitalSubsemiring.extCITED BYCITES

Cites3

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Cited by6

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