Theorems · Theorem · ring theory

NonUnitalRingHom.srange_eq_top_iff_surjective

∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocSemiring R] {F : Type u_1} [inst_1 : FunLike F R S]
  [inst_2 : NonUnitalNonAssocSemiring S] [inst_3 : NonUnitalRingHomClass F R S] {f : F},
  NonUnitalRingHom.srange f = ⊤ ↔ Function.Surjective ⇑f

Defined in: Mathlib.RingTheory.NonUnitalSubsemiring.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NonUnitalNonAssocSemiring FunLike NonUnitalNonAssocSemiring NonUnitalRingHomClass

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Cites15

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

DFunLike.coestatement and proof · cited by 62,936
Setproof · cited by 53,352
Top.topstatement and proof · cited by 9,680
SetLike.coeproof · cited by 8,199
Set.rangeproof · cited by 4,705
Set.univproof · cited by 3,945
FunLikestatement and proof · cited by 2,560
NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
NonUnitalSubsemiringstatement · cited by 201
NonUnitalRingHomClassstatement and proof · cited by 82
SetLike.ext'_iffproof · cited by 78
Set.range_eq_univproof · cited by 50

Cited by1

Results whose statement or proof uses this declaration.

NonUnitalRingHom.srange_eq_top_of_surjectiveproof · cited by 2