Theorems · Theorem · order theory
Int.floor_div_cast_of_nonneg
∀ {k : Type u_4} [inst : Field k] [inst_1 : LinearOrder k] [IsOrderedRing k] [inst_3 : FloorRing k] {n : ℤ},
0 ≤ n → ∀ (a : k), ⌊a / ↑n⌋ = ⌊a⌋ / n- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 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.
Cites13
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
- IsOrderedRingstatement and proof · cited by 777
- ne_of_gtproof · cited by 637
- FloorRingstatement and proof · cited by 405
- div_zeroproof · cited by 251
- Int.floorstatement and proof · cited by 225
- LE.le.eq_or_ltproof · cited by 220
- Int.cast_zeroproof · cited by 188
- div_mul_cancel₀proof · cited by 122
- Int.cast_posproof · cited by 24
- Int.floor_zeroproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Int.floor_div_natCastproof · cited by 0