Theorems · Theorem · order theory
Int.cast_pos
∀ {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
- 24 results in Mathlib
- Foundations
- Depth 44 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.
- PartialOrderstatement and proof · cited by 6,410
- AddLeftMonostatement and proof · cited by 687
- ZeroLEOneClassstatement and proof · cited by 304
- Int.cast_zeroproof · cited by 188
- AddCommGroupWithOnestatement and proof · cited by 61
- Int.cast_ltproof · cited by 14
Cited by24
Results whose statement or proof uses this declaration.
- EisensteinSeries.summable_norm_eisSummandproof · cited by 4
- Int.mul_cast_floor_div_cancel_of_posproof · cited by 3
- Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zeroproof · cited by 3
- Liouville.irrationalproof · cited by 3
- Pell.exists_of_not_isSquareproof · cited by 3
- eventually_residual_liouvilleproof · cited by 2
- Int.Ico_filter_dvd_eqproof · cited by 2
- Int.Ioc_filter_dvd_eqproof · cited by 2
- Int.floor_div_cast_of_nonnegproof · cited by 1
- Int.ceil_div_ceil_inv_sub_oneproof · cited by 1
- Rat.cast_pos_of_posproof · cited by 1
- Real.exists_rat_abs_sub_le_and_den_leproof · cited by 1