Theorems · Definition · number theory
NNRat.cast
{K : Type u_1} → [NNRatCast K] → ℚ≥0 → KCanonical homomorphism from ℚ≥0 to a division semiring K.
This is just the bare function in order to aid in creating instances of DivisionSemiring.
- Defined in
- Mathlib.Data.Rat.Init
- Cited by
- 235 results in Mathlib
- Foundations
- Depth 41 from the axioms, rests on 323 definitions · uses propext, Quot.sound
- Assumes
- NNRatCast
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRatstatement · cited by 523
- NNRatCaststatement and proof · cited by 11
- NNRatCast.nnratCastproof · cited by 2
Cited by275
Results whose statement or proof uses this declaration.
- NNRat.numproof · cited by 53
- NNRat.denproof · cited by 51
- NNRat.cast_natCaststatement · cited by 31
- Ideal.Quotient.fieldproof · cited by 25
- NNRat.extstatement · cited by 18
- NNRat.cast_defstatement · cited by 17
- NNRat.num_coestatement and proof · cited by 14
- NNRat.castOrderEmbeddingproof · cited by 12
- NNRat.castHomproof · cited by 10
- NNRat.cast_divstatement · cited by 7
- NNRat.smul_defstatement · cited by 7
- NNRat.cast_nonnegstatement · cited by 6
Showing the 200 most cited of 275.