Theorems · Theorem · order theory
Int.lt_floor_add_one
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] (a : R), a < ↑⌊a⌋ + 1- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingLinearOrderFloorRing
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
- FloorRingstatement and proof · cited by 405
- Int.cast_oneproof · cited by 371
- Int.floorstatement and proof · cited by 225
- Int.cast_addproof · cited by 124
- Int.lt_succ_floorproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Int.sub_one_lt_floorproof · cited by 6
- Int.sub_floor_div_mul_ltproof · cited by 4
- Int.abs_sub_lt_one_of_floor_eq_floorproof · cited by 3
- abs_sub_roundproof · cited by 2
- continuousAt_fractproof · cited by 1
- tendsto_floor_right_pure_floorproof · cited by 1
- CircleDeg1Lift.map_lt_add_floor_translationNumber_add_oneproof · cited by 1
- Int.mul_lt_floorproof · cited by 1
- LinearGrowth.Real.eventually_atTop_exists_int_betweenproof · cited by 1
- Int.ceil_le_floor_add_oneproof · cited by 1
- Irrational.beattySeq'_pos_eqproof · cited by 1
- liouvilleWith_oneproof · cited by 0