Theorems · Theorem · commutative algebra
RingHom.coe_rangeS
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] (f : R →+* S),
↑f.rangeS = Set.range ⇑f- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- RingHomstatement and proof · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Set.rangestatement · cited by 4,705
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- RingHom.rangeSstatement and proof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- RingHom.rangeS_top_iff_surjectiveproof · cited by 1
- Subsemiring.rangeS_subtypeproof · cited by 1
- Subfield.fieldRange_subtypeproof · cited by 1
- Subring.range_subtypeproof · cited by 1
- RingHom.rangeS_eq_topproof · cited by 1
- Subsemiring.coe_botproof · cited by 0