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Theorems · Theorem · ring theory

NonUnitalSubring.mem_closure

∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {x : R} {s : Set R},
  x ∈ NonUnitalSubring.closure s ↔ ∀ (S : NonUnitalSubring R), s ⊆ ↑S → x ∈ S
Defined in
Mathlib.RingTheory.NonUnitalSubring.Basic
Cited by
1 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalNonAssocRing
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Around this declaration

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

NonUnitalSubring.subset_closure · cited by 9NonUnitalSubring.subset_c…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeNonUnitalNonAssocRing · cited by 354NonUnitalNonAssocRingNonUnitalSubring · cited by 185NonUnitalSubringNonUnitalSubring.closure · cited by 23NonUnitalSubring.closureNonUnitalSubring.mem_sInf · cited by 1NonUnitalSubring.mem_sInfNonUnitalSubring.mem_closureCITED BYCITES

Cites6

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Cited by1

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