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Theorems · Theorem · number theory

Rat.cast_fract

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] (x : ℚ),
  ↑(Int.fract x) = Int.fract ↑x
Defined in
Mathlib.Data.Rat.Floor
Cited by
1 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRingFloorRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

GenContFract.IntFractPair.coe_of_rat_eq · cited by 1IntFractPair.coe_of_rat_eqLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingFloorRing · cited by 405FloorRingInt.floor · cited by 225Int.floorInt.fract · cited by 114Int.fractRat.cast_intCast · cited by 74Rat.cast_intCastRat.cast_sub · cited by 9Rat.cast_subRat.floor_cast · cited by 8Rat.floor_castRat.cast_fractCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.