Theorems · Theorem · order theory
toIocDiv_eq_neg_floor
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] [inst_3 : FloorRing α]
{p : α} (hp : 0 < p) (a b : α), toIocDiv hp a b = -⌊(a + p - b) / p⌋- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- neg_mulproof · cited by 654
- FloorRingstatement and proof · cited by 405
- sub_neg_eq_addproof · cited by 264
- Int.floorstatement and proof · cited by 225
- Int.cast_negproof · cited by 224
- sub_nonnegproof · cited by 167
- zsmul_eq_mulproof · cited by 120
Cited by2
Results whose statement or proof uses this declaration.
- Complex.arg_mul_cos_add_sin_mul_I_subproof · cited by 1
- toIocMod_eq_sub_fract_mulproof · cited by 0