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Theorems · Definition · ring theory

NonUnitalSubsemiring.copy

{R : Type u} →
  [inst : NonUnitalNonAssocSemiring R] → (S : NonUnitalSubsemiring R) → (s : Set R) → s = ↑S → NonUnitalSubsemiring R

Copy of a non-unital subsemiring with a new carrier equal to the old one. Useful to fix definitional equalities.

Defined in
Mathlib.RingTheory.NonUnitalSubsemiring.Defs
Cited by
4 results in Mathlib
Foundations
Depth 14 from the axioms · uses no axioms
Assumes
NonUnitalNonAssocSemiring
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Around this declaration

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

NonUnitalRingHom.srange · cited by 17NonUnitalRingHom.srangeNonUnitalSubalgebra.copy · cited by 3NonUnitalSubalgebra.copyNonUnitalSubring.copy · cited by 2NonUnitalSubring.copyNonUnitalStarSubsemiring.copy · cited by 2NonUnitalStarSubsemiring.…NonUnitalSubalgebra.coe_iSup_of_directed · cited by 2NonUnitalSubalgebra.coe_i…NonUnitalSubsemiring.copy.congr_simp · cited by 0copy.congr_simpNonUnitalSubsemiring.copy_eq · cited by 0NonUnitalSubsemiring.copy…NonUnitalSubsemiring.coe_copy · cited by 0NonUnitalSubsemiring.coe_…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeAddSubmonoid · cited by 1178AddSubmonoidNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringSubsemigroup · cited by 323SubsemigroupNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringNonUnitalSubsemiring.toAddSubmonoid · cited by 56NonUnitalSubsemiring.toAd…NonUnitalSubsemiring.toSubsemigroup · cited by 12NonUnitalSubsemiring.toSu…AddSubmonoid.copy · cited by 3AddSubmonoid.copySubsemigroup.copy · cited by 2Subsemigroup.copyNonUnitalSubsemiring.copyCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.