Theorems · Theorem · number theory
Rat.ceil_intCast_div_natCast
∀ (n : ℤ) (d : ℕ), ⌈↑n / ↑d⌉ = -(-n / ↑d)
- Defined in
- Mathlib.Data.Rat.Floor
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- neg_negproof · cited by 960
- Int.floorproof · cited by 225
- Int.cast_negproof · cited by 224
- neg_divproof · cited by 161
- Int.ceilstatement and proof · cited by 138
- Rat.floor_intCast_div_natCastproof · cited by 5
- Int.floor_negproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Rat.isInt_intCeil_ofIsRat_negproof · cited by 0
- Rat.isInt_intFloor_ofIsRat_negproof · cited by 0
- Rat.ceil_natCast_div_natCastproof · cited by 0
- Rat.isNat_intCeil_ofIsNNRatproof · cited by 0