Theorems · Theorem · field theory
NNRat.cast_def
∀ {K : Type u_1} [inst : DivisionSemiring K] (q : ℚ≥0), ↑q = ↑q.num / ↑q.den- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRatstatement and proof · cited by 523
- NNRat.caststatement · cited by 235
- DivisionSemiringstatement and proof · cited by 216
- NNRat.numstatement · cited by 53
- NNRat.denstatement · cited by 51
- DivisionSemiring.nnratCast_defproof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- NNRat.cast_natCastproof · cited by 31
- NNRat.cast_nonnegproof · cited by 6
- map_nnratCastproof · cited by 5
- NNRat.cast_divNat_of_ne_zeroproof · cited by 4
- NNRat.num_div_denproof · cited by 3
- NNRat.cast_strictMonoproof · cited by 3
- map_nnratCast_smulproof · cited by 2
- NNRat.cast_commuteproof · cited by 2
- SubfieldClass.nnratCast_memproof · cited by 2
- Rat.cast_nnratCastproof · cited by 1
- NNRat.cast_add_of_ne_zeroproof · cited by 1
- NNRat.cast_injectiveproof · cited by 1