Theorems · Theorem · number theory
NNRat.cast_le
∀ {K : Type u_5} [inst : Semifield K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {p q : ℚ≥0}, ↑p ≤ ↑q ↔ p ≤ q- Defined in
- Mathlib.Data.Rat.Cast.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- NNRatstatement and proof · cited by 523
- Semifieldstatement and proof · cited by 439
- NNRat.caststatement · cited by 235
- OrderEmbedding.le_iff_leproof · cited by 32
- NNRat.castOrderEmbeddingproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- NNRat.cast_le_natCastproof · cited by 1
- NNRat.ofNat_le_castproof · cited by 0
- NNRat.natCast_le_castproof · cited by 0
- NNRat.cast_le_ofNatproof · cited by 0