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Theorems · Theorem · ring theory

NonUnitalSubring.closure_eq

∀ {R : Type u} [inst : NonUnitalNonAssocRing R] (s : NonUnitalSubring R), NonUnitalSubring.closure ↑s = s

Closure of a NonUnitalSubring S equals S.

Defined in
Mathlib.RingTheory.NonUnitalSubring.Basic
Cited by
1 results in Mathlib
Foundations
Depth 74 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.closure_univ · cited by 0NonUnitalSubring.closure_…SetLike.coe · cited by 8199SetLike.coeNonUnitalNonAssocRing · cited by 354NonUnitalNonAssocRingNonUnitalSubring · cited by 185NonUnitalSubringGaloisInsertion.l_u_eq · cited by 37GaloisInsertion.l_u_eqNonUnitalSubring.closure · cited by 23NonUnitalSubring.closureNonUnitalSubring.gi · cited by 6NonUnitalSubring.giNonUnitalSubring.closure_eqCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.