Theorems · Theorem · number theory
Rat.isNat_intFract_of_isInt
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [inst_3 : FloorRing R] (r : R)
(m : ℤ), Mathlib.Meta.NormNum.IsInt r m → Mathlib.Meta.NormNum.IsNat (Int.fract r) 0- Defined in
- Mathlib.Data.Rat.Floor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- Nat.cast_zeroproof · cited by 1,870
- FloorRingstatement and proof · cited by 405
- Int.fractstatement · cited by 114
- Int.fract_intCastproof · cited by 8
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