Theorems · Theorem · commutative algebra
Subsemiring.one_mem
∀ {R : Type u} [inst : NonAssocSemiring R] (s : Subsemiring R), 1 ∈ sA subsemiring contains the semiring's 1.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- OneMemClass.one_memproof · cited by 87
Cited by3
Results whose statement or proof uses this declaration.
- Subring.one_mem_toNonUnitalSubringproof · cited by 0
- IsLocalization.isInteger_oneproof · cited by 0
- Subsemiring.toNonUnitalSubsemiring_toSubsemiringstatement · cited by 0