Theorems · Theorem · order theory
Int.fract_nonneg
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R),
0 ≤ Int.fract a- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, 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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- sub_nonnegproof · cited by 167
- Int.fractstatement · cited by 114
- Int.floor_leproof · cited by 30
Cited by17
Results whose statement or proof uses this declaration.
- Int.fract_eq_iffproof · cited by 4
- GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_oneproof · cited by 4
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- Int.abs_fractproof · cited by 2
- Int.fract_div_mul_self_mem_Icoproof · cited by 2
- Int.fract_eq_zero_or_add_one_sub_ceilproof · cited by 2
- Int.fract_fractproof · cited by 2
- CircleDeg1Lift.forall_map_sub_of_Iccproof · cited by 2
- Int.fract_posproof · cited by 2
- GenContFract.IntFractPair.exists_nth_stream_eq_none_of_ratproof · cited by 1
- Int.image_fractproof · cited by 1
- tendsto_fract_rightproof · cited by 1