Theorems · Definition · order theory
Int.floor
{α : Type u_2} → [inst : Ring α] → [inst_1 : LinearOrder α] → [FloorRing α] → α → ℤInt.floor a is the greatest integer z such that z ≤ a. It is denoted with ⌊a⌋.
- Defined in
- Mathlib.Algebra.Order.Floor.Defs
- Cited by
- 225 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 6 definitions · uses no axioms
- Assumes
- RingLinearOrderFloorRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- FloorRing.floorproof · cited by 3
Cited by231
Results whose statement or proof uses this declaration.
- Int.fractproof · cited by 114
- roundproof · cited by 49
- Int.floor_lestatement · cited by 30
- Int.le_floorstatement · cited by 22
- GenContFract.IntFractPair.ofproof · cited by 22
- Int.floor_eq_iffstatement and proof · cited by 15
- Int.floor_intCaststatement · cited by 14
- Int.lt_floor_add_onestatement and proof · cited by 12
- ZSpan.floorproof · cited by 10
- Int.ceil_add_intCastproof · cited by 8
- Int.floor_add_intCaststatement and proof · cited by 8
- round_eqstatement and proof · cited by 8
Showing the 200 most cited of 231.