Theorems · Theorem · number theory
Rat.cast_nonneg
∀ {q : ℚ} {K : Type u_5} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K], 0 ≤ ↑q ↔ 0 ≤ q- Defined in
- Mathlib.Data.Rat.Cast.Order
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.cast_zeroproof · cited by 1,870
- Rat.cast_zeroproof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- irrational_sqrt_ratCast_iff_of_nonnegproof · cited by 3
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- NumberField.mixedEmbedding.covolume_idealLatticeproof · cited by 1
- ENNReal.lt_iff_exists_real_btwnproof · cited by 1
- NNReal.lt_iff_exists_rat_btwnproof · cited by 1