Theorems · Theorem · ring theory
AlgHom.range_comp_le_range
∀ {R : Type u} {A : Type v} {B : Type w} {C : Type w'} [inst : CommSemiring R] [inst_1 : Semiring A]
[inst_2 : Algebra R A] [inst_3 : Semiring B] [inst_4 : Algebra R B] [inst_5 : Semiring C] [inst_6 : Algebra R C]
(f : A →ₐ[R] B) (g : B →ₐ[R] C), (g.comp f).range ≤ g.range- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
- AlgHom.compstatement and proof · cited by 501
- AlgHom.rangestatement and proof · cited by 169
- Set.range_comp_subset_rangeproof · cited by 32
- SetLike.coe_monoproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.TensorProduct.map_rangeproof · cited by 3
- IntermediateField.LinearDisjoint.of_le_right'proof · cited by 1