Theorems · Theorem · number theory
Rat.isInt_intFloor_ofIsRat_neg
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] (r : α)
(n d : ℕ),
Mathlib.Meta.NormNum.IsRat r (Int.negOfNat n) d → Mathlib.Meta.NormNum.IsInt ⌊r⌋ (Int.negOfNat (-(-↑n / ↑d)).toNat)- Defined in
- Mathlib.Data.Rat.Floor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- neg_negproof · cited by 960
- Invertibleproof · cited by 549
- FloorRingstatement and proof · cited by 405
- Int.cast_natCastproof · cited by 393
- Invertible.invOfproof · cited by 268
- Int.floorstatement and proof · cited by 225
- Int.ceilproof · cited by 138
- Nat.cast_nonnegproof · cited by 109
- div_nonnegproof · cited by 103
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