Theorems · Theorem · order theory
Int.cast_nonneg_iff
∀ {R : Type u_1} [inst : AddCommGroupWithOne R] [inst_1 : PartialOrder R] [AddLeftMono R] [ZeroLEOneClass R] [NeZero 1]
{n : ℤ}, 0 ≤ ↑n ↔ 0 ≤ n- Defined in
- Mathlib.Algebra.Order.Ring.Cast
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Nat.cast_oneproof · cited by 2,501
- AddLeftMonostatement and proof · cited by 687
- zero_lt_oneproof · cited by 598
- Nat.cast_addproof · cited by 586
- lt_of_le_of_ltproof · cited by 432
- Int.cast_natCastproof · cited by 393
- LT.lt.not_geproof · cited by 305
- ZeroLEOneClassstatement and proof · cited by 304
- neg_add_revproof · cited by 236
- AddCommGroupWithOnestatement and proof · cited by 61
- Int.cast_negSuccproof · cited by 32
Cited by4
Results whose statement or proof uses this declaration.
- Int.cast_leproof · cited by 28
- Polynomial.Chebyshev.abs_eval_T_real_eq_one_iffproof · cited by 3
- NumberField.sign_discrproof · cited by 1
- irrational_sqrt_intCast_iffproof · cited by 0