Theorems · Theorem · order theory
Int.mul_cast_floor_div_cancel_of_pos
∀ {R : Type u_4} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [inst_3 : FloorRing R] {n : ℤ},
0 < n → ∀ (a : R), ⌊a * ↑n⌋ / n = ⌊a⌋- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 50 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
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- FloorRingstatement and proof · cited by 405
- Int.floorstatement and proof · cited by 225
- Int.cast_mulproof · cited by 113
- eq_of_forall_le_iffproof · cited by 65
- Int.cast_posproof · cited by 24
- Int.le_floorproof · cited by 22
- mul_le_mul_iff_of_pos_rightproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Int.mul_natCast_floor_div_cancelproof · cited by 1
- Int.floor_div_cast_of_nonnegproof · cited by 1
- Int.cast_mul_floor_div_cancel_of_posproof · cited by 1