Theorems · Theorem · order theory
Int.sub_one_lt_floor
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R), a - 1 < ↑⌊a⌋- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 39 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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsOrderedRingstatement and proof · cited by 777
- FloorRingstatement and proof · cited by 405
- Int.floorstatement · cited by 225
- sub_lt_iff_lt_addproof · cited by 39
- Int.lt_floor_add_oneproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- Int.fract_lt_oneproof · cited by 20
- Real.exists_isLUBproof · cited by 3
- CircleDeg1Lift.tendsto_atTopproof · cited by 1
- CircleDeg1Lift.lt_map_map_zeroproof · cited by 1
- Int.le_floor_add_floorproof · cited by 1
- sub_half_lt_roundproof · cited by 0