Theorems · Theorem · logic and foundations
Ordinal.div_le
∀ {a b c : Ordinal.{u_4}}, b ≠ 0 → (a / b ≤ c ↔ a < b * Order.succ c)- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Ordinalstatement and proof · cited by 1,688
- Order.succstatement and proof · cited by 633
- Order.lt_succ_iffproof · cited by 22
- Ordinal.lt_mul_iff_div_ltproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Ordinal.mul_add_divproof · cited by 4
- Ordinal.div_eq_zero_of_ltproof · cited by 2
- Ordinal.div_le_of_le_mulproof · cited by 2
- Ordinal.lt_divproof · cited by 1
- Ordinal.div_eqproof · cited by 1
- Ordinal.natCast_divproof · cited by 1