Theorems · Theorem · order theory
Int.ceil_div_ceil_inv_sub_one
∀ {k : Type u_4} [inst : Field k] [inst_1 : LinearOrder k] [IsOrderedRing k] [inst_3 : FloorRing k] {a : k},
1 ≤ a → ⌈↑⌈(a - 1)⁻¹⌉ / a⌉ = ⌈(a - 1)⁻¹⌉- Defined in
- Mathlib.Algebra.Order.Floor.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- Fieldstatement and proof · cited by 7,404
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- sub_selfproof · cited by 996
- one_ne_zeroproof · cited by 885
- IsOrderedRingstatement and proof · cited by 777
Cited by1
Results whose statement or proof uses this declaration.
- Int.ceil_le_mulproof · cited by 1