Theorems · Theorem · number theory
Rat.floor_cast
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : FloorRing α] (x : ℚ),
⌊↑x⌋ = ⌊x⌋- Defined in
- Mathlib.Data.Rat.Floor
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- Int.floorstatement and proof · cited by 225
- Int.floor_eq_iffproof · cited by 15
Cited by8
Results whose statement or proof uses this declaration.
- Rat.round_castproof · cited by 3
- Rat.ceil_castproof · cited by 2
- Rat.cast_fractproof · cited by 1
- GenContFract.IntFractPair.coe_of_rat_eqproof · cited by 1
- Rat.isNat_intFloor_ofIsNNRatproof · cited by 0
- GenContFract.coe_of_h_rat_eqproof · cited by 0
- GenContFract.coe_of_rat_eqproof · cited by 0
- Rat.isInt_intFloor_ofIsRat_negproof · cited by 0