Theorems · Theorem · order theory
Int.floor_le
∀ {α : Type u_2} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] (a : α), ↑⌊a⌋ ≤ a- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- FloorRingstatement and proof · cited by 405
- Int.floorstatement · cited by 225
- GaloisConnection.l_u_leproof · cited by 36
- Int.gc_coe_floorproof · cited by 3
Cited by30
Results whose statement or proof uses this declaration.
- Int.fract_nonnegproof · cited by 17
- ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_forall_integrable_exp_mulproof · cited by 4
- Int.sub_floor_div_mul_nonnegproof · cited by 4
- Real.exists_isLUBproof · cited by 3
- Int.abs_sub_lt_one_of_floor_eq_floorproof · cited by 3
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- abs_sub_roundproof · cited by 2
- Real.natLog_le_logbproof · cited by 2
- Real.floor_logb_natCastproof · cited by 2
- CircleDeg1Lift.le_map_of_map_zeroproof · cited by 2
- GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_invproof · cited by 1
- CircleDeg1Lift.map_lt_add_translationNumber_add_oneproof · cited by 1