Theorems · Theorem · order theory
Int.le_floor
∀ {α : Type u_2} [inst : Ring α] [inst_1 : LinearOrder α] [inst_2 : FloorRing α] {z : ℤ} {a : α}, z ≤ ⌊a⌋ ↔ ↑z ≤ a- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 22 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.
Cites5
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
- Int.gc_coe_floorproof · cited by 3
Cited by22
Results whose statement or proof uses this declaration.
- Int.floor_eq_iffproof · cited by 15
- Int.floor_intCastproof · cited by 14
- Int.floor_add_intCastproof · cited by 8
- Int.floor_ltproof · cited by 7
- Int.floor_nonnegproof · cited by 5
- Int.floor_natCastproof · cited by 4
- Int.mul_cast_floor_div_cancel_of_posproof · cited by 3
- Int.floor_negproof · cited by 3
- round_leproof · cited by 3
- Real.floor_logb_natCastproof · cited by 2
- Rat.den_le_and_le_num_le_of_sub_lt_one_div_den_sqproof · cited by 1
- Int.floor_congrproof · cited by 1