Theorems · Theorem · number theory
Rat.cast_abs
∀ {K : Type u_5} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] (q : ℚ), ↑|q| = |↑q|- Defined in
- Mathlib.Data.Rat.Cast.Order
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement · cited by 1,814
- Rat.cast_negproof · cited by 25
- Rat.cast_maxproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.prod_eq_abs_normproof · cited by 8
- SimpleGraph.not_isUniform_iffproof · cited by 5
- Rat.mulHeight_eq_max_abs_of_gcd_eq_oneproof · cited by 2
- NumberField.abs_discr_gt_twoproof · cited by 2
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_leproof · cited by 2
- Rat.AbsoluteValue.real_eq_absproof · cited by 2
- LiouvilleWith.mul_ratproof · cited by 2
- Rat.infinitePlace_applyproof · cited by 2
- NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_normproof · cited by 1
- NumberField.FinitePlace.prod_eq_inv_abs_normproof · cited by 1
- NumberField.mixedEmbedding.norm_eq_zero_iff'proof · cited by 1
- Rat.uniformContinuous_absproof · cited by 0