Theorems · Theorem · field theory
RingHom.ext_rat
∀ {F : Type u_1} {R : Type u_5} [inst : Semiring R] [inst_1 : FunLike F ℚ R] [RingHomClass F ℚ R] (f g : F), f = gAny two ring homomorphisms from ℚ to a semiring are equal. If the codomain is a division ring,
then this lemma follows from eq_ratCast.
- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringFunLikeRingHomClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- FunLikestatement and proof · cited by 2,560
- RingHom.compproof · cited by 899
- RingHomClass.toRingHomproof · cited by 746
- Int.castRingHomproof · cited by 254
- RingHomClassstatement and proof · cited by 193
- RingHom.congr_funproof · cited by 29
- RingHom.ext_intproof · cited by 25
- MonoidWithZeroHomClass.ext_rat'proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- wittStructureRat_propproof · cited by 4
- wittStructureRat_existsUniqueproof · cited by 1