Theorems · Theorem · ring theory
RingHom.congr_fun
∀ {α : Type u_2} {β : Type u_3} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β} {f g : α →+* β},
f = g → ∀ (x_2 : α), f x_2 = g x_2- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
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
- NonAssocSemiringstatement and proof · cited by 805
- DFunLike.congr_funproof · cited by 288
Cited by29
Results whose statement or proof uses this declaration.
- RingHomCompTriple.comp_applyproof · cited by 42
- IsLocalization.ringHom_extproof · cited by 32
- Ideal.Quotient.ringHom_extproof · cited by 17
- Polynomial.ringHom_ext'proof · cited by 14
- NumberField.ComplexEmbedding.IsConj.eqproof · cited by 5
- AddMonoidAlgebra.ringHom_ext'proof · cited by 5
- NumberField.ComplexEmbedding.IsReal.compproof · cited by 3
- MvPolynomial.eval₂Hom_zero_applyproof · cited by 3
- NumberField.IsTotallyReal.le_maximalRealSubfieldproof · cited by 3
- NumberField.is_primitive_element_of_infinitePlace_ltproof · cited by 3
- RingHom.ext_ratproof · cited by 2
- Algebra.EssFiniteType.algHom_extproof · cited by 2