Theorems · Theorem · field theory
MonoidWithZeroHomClass.ext_nnrat
∀ {M₀ : Type u_5} [inst : MonoidWithZero M₀] {f g : ℚ≥0 →*₀ M₀},
f.comp (MonoidWithZeroHom.ofClass (Nat.castRingHom ℚ≥0)) = g.comp (MonoidWithZeroHom.ofClass (Nat.castRingHom ℚ≥0)) →
f = gIf monoid with zero homs f and g from ℚ≥0 agree on the naturals then they are equal.
See note [partially-applied ext lemmas] for why comp is used here.
- Defined in
- Mathlib.Data.Rat.Cast.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZero
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.
- RingHomstatement · cited by 10,189
- MonoidWithZeroHomstatement and proof · cited by 704
- NNRatstatement and proof · cited by 523
- MonoidWithZerostatement and proof · cited by 456
- DFunLike.congr_funproof · cited by 288
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.compstatement and proof · cited by 34
- Nat.castRingHomstatement and proof · cited by 27
- MonoidWithZeroHomClass.ext_nnrat'proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MonoidWithZeroHomClass.ext_nnrat_iffproof · cited by 0