Theorems · Theorem · order theory
Int.floor_intCast
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsOrderedRing R] (z : ℤ), ⌊↑z⌋ = z- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.floorstatement · cited by 225
- eq_of_forall_le_iffproof · cited by 65
- Int.cast_leproof · cited by 28
- Int.le_floorproof · cited by 22
Cited by14
Results whose statement or proof uses this declaration.
- Int.fract_intCastproof · cited by 8
- Int.floor_zeroproof · cited by 6
- round_intCastproof · cited by 2
- Int.floor_oneproof · cited by 2
- Int.floor_eq_self_iff_memproof · cited by 2
- tendsto_floor_atTopproof · cited by 1
- tendsto_floor_right_pureproof · cited by 1
- tendsto_ceil_right_pure_add_oneproof · cited by 1
- GenContFract.convs'_of_intproof · cited by 1
- GenContFract.convs'_succproof · cited by 1
- tendsto_floor_atBotproof · cited by 1
- ZSpan.floor_eq_self_of_memproof · cited by 0