Theorems · Theorem · ring theory
RingHom.map_sub
∀ {α : Type u_2} {β : Type u_3} [inst : NonAssocRing α] [inst_1 : NonAssocRing β] (f : α →+* β) (x y : α),
f (x - y) = f x - f yRing homomorphisms preserve subtraction.
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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
- map_subproof · cited by 565
- NonAssocRingstatement and proof · cited by 483
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.map_subproof · cited by 49
- Polynomial.coe_subproof · cited by 4
- LinearPMap.mkSpanSingleton'_applyproof · cited by 3
- IsLocalRing.of_surjective'proof · cited by 3
- IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_oneproof · cited by 2
- char_dvd_card_solutions_of_sum_ltproof · cited by 2
- MvPolynomial.eval₂_subproof · cited by 2
- ZMod.cast_subproof · cited by 1
- QuaternionAlgebra.coe_subproof · cited by 1
- PowerSeries.coe_subproof · cited by 1
- Polynomial.irreducible_compproof · cited by 1
- GaussianInt.toComplex_subproof · cited by 0