Theorems · Theorem · order theory
Int.fract_div_mul_self_mem_Ico
∀ {k : Type u_4} [inst : Field k] [inst_1 : LinearOrder k] [IsOrderedRing k] [inst_3 : FloorRing k] (a b : k),
0 < a → Int.fract (b / a) * a ∈ Set.Ico 0 a- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- Set.Icostatement · cited by 799
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.fractstatement · cited by 114
- Int.fract_lt_oneproof · cited by 20
- Int.fract_nonnegproof · cited by 17
- mul_nonneg_iff_of_pos_rightproof · cited by 5
- mul_lt_iff_lt_one_leftproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Function.Periodic.sInf_add_zsmul_le_integral_of_posproof · cited by 1
- Function.Periodic.integral_le_sSup_add_zsmul_of_posproof · cited by 1