Theorems · Theorem · order theory
Int.ceil_lt_add_one
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (a : R), ↑⌈a⌉ < a + 1- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.cast_oneproof · cited by 371
- Int.ceilstatement and proof · cited by 138
- lt_add_oneproof · cited by 105
- Int.ceil_add_intCastproof · cited by 8
- Int.lt_ceilproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Int.ceil_lt_mulproof · cited by 2
- tendsto_floor_left_pure_ceil_sub_oneproof · cited by 1
- CircleDeg1Lift.tendsto_atBotproof · cited by 1
- Int.ceil_div_ceil_inv_sub_oneproof · cited by 1
- CircleDeg1Lift.map_map_zero_ltproof · cited by 1
- tendsto_ceil_left_pure_ceilproof · cited by 1
- Int.ceil_add_ceil_leproof · cited by 0