Theorems · Theorem · ring theory
RingHom.comp_apply
∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β}
{x_2 : NonAssocSemiring γ} (hnp : β →+* γ) (hmn : α →+* β) (x_3 : α), (hnp.comp hmn) x_3 = hnp (hmn x_3)- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- RingHom.compstatement · cited by 899
- NonAssocSemiringstatement and proof · cited by 805
Cited by41
Results whose statement or proof uses this declaration.
- IsScalarTower.algebraMap_applyproof · cited by 116
- Ideal.Quotient.factor_comp_applyproof · cited by 5
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3
- WittVector.truncate_comp_liftproof · cited by 3
- AdjoinRoot.minpoly_rootproof · cited by 3
- Polynomial.map_smulproof · cited by 3
- PadicInt.lift_specproof · cited by 3
- RootPairing.algebraMap_pairingIn'proof · cited by 2
- PadicInt.pow_dvd_nthHom_subproof · cited by 2
- RingHomInvPair.comp_apply_eq₂proof · cited by 2
- Ideal.Quotient.factor_comp_mkproof · cited by 2
- AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mkproof · cited by 2