Theorems · Theorem · order theory
Int.sub_floor_div_mul_lt
∀ {k : Type u_4} [inst : Field k] [inst_1 : LinearOrder k] [IsOrderedRing k] [inst_3 : FloorRing k] {b : k} (a : k),
0 < b → a - ↑⌊a / b⌋ * b < b- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 4 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.
Cites10
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
- add_commproof · cited by 1,535
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.floorstatement and proof · cited by 225
- div_lt_iff₀proof · cited by 45
- sub_lt_iff_lt_addproof · cited by 39
- Int.lt_floor_add_oneproof · cited by 12
- one_add_mulproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Real.sin_eq_zero_iffproof · cited by 5
- toIocDiv_eq_neg_floorproof · cited by 2
- toIcoDiv_eq_floorproof · cited by 2
- UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStripproof · cited by 1