Theorems · Theorem · ring theory

NonUnitalSubsemiringClass.mul_mem

∀ {S : Type u_1} {R : outParam (Type u)} {inst : NonUnitalNonAssocSemiring R} {inst_1 : SetLike S R}
  [self : NonUnitalSubsemiringClass S R] {s : S} {a b : R}, a ∈ s → b ∈ s → a * b ∈ s

Defined in: Mathlib.RingTheory.NonUnitalSubsemiring.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: NonUnitalSubsemiringClass

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SetLikestatement and proof · cited by 1,084
NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
NonUnitalSubsemiringClassstatement and proof · cited by 22

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