Theorems · Theorem · order theory
Int.cast_le
∀ {R : Type u_1} [inst : AddCommGroupWithOne R] [inst_1 : PartialOrder R] [AddLeftMono R] [ZeroLEOneClass R] [NeZero 1]
{m n : ℤ}, ↑m ≤ ↑n ↔ m ≤ n- Defined in
- Mathlib.Algebra.Order.Ring.Cast
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 41 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.
- PartialOrderstatement and proof · cited by 6,410
- AddLeftMonostatement and proof · cited by 687
- ZeroLEOneClassstatement and proof · cited by 304
- sub_nonnegproof · cited by 167
- Int.cast_subproof · cited by 78
- AddCommGroupWithOnestatement and proof · cited by 61
- Int.cast_nonneg_iffproof · cited by 4
Cited by28
Results whose statement or proof uses this declaration.
- Int.floor_intCastproof · cited by 14
- Int.ceil_intCastproof · cited by 11
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Int.floor_natCastproof · cited by 4
- NumberField.Embeddings.finite_of_norm_leproof · cited by 4
- Real.exists_isLUBproof · cited by 3
- NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBddproof · cited by 2
- NumberField.abs_discr_ge'proof · cited by 2
- summable_jacobiTheta₂'_term_iffproof · cited by 2
- summable_jacobiTheta₂_term_fderiv_iffproof · cited by 2
- Int.cast_le_neg_one_of_negproof · cited by 2
- Int.comap_cast_atBotproof · cited by 2