Theorems · Theorem · number theory
Rat.cast_le
∀ {p q : ℚ} {K : Type u_5} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K], ↑p ≤ ↑q ↔ p ≤ q- Defined in
- Mathlib.Data.Rat.Cast.Order
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 81 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
- OrderEmbedding.le_iff_leproof · cited by 32
- Rat.castOrderEmbeddingproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- NumberField.Units.dirichletUnitTheorem.seq_nextproof · cited by 3
- Padic.isUniformInducing_cast_withValproof · cited by 2
- Rat.comap_cast_atBotproof · cited by 2
- Rat.comap_cast_atTopproof · cited by 2
- Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sqproof · cited by 1
- Rat.intCast_le_castproof · cited by 0
- Rat.natCast_le_castproof · cited by 0
- Rat.cast_le_intCastproof · cited by 0
- Rat.cast_le_natCastproof · cited by 0