Theorems · Theorem · logic and foundations
Ordinal.mul_le_iff_of_isSuccLimit
∀ {a b c : Ordinal.{u_4}}, Order.IsSuccLimit b → (a * b ≤ c ↔ ∀ b' < b, a * b' ≤ c)- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 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.
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Ordinalstatement and proof · cited by 1,688
- le_of_not_gtproof · cited by 430
- Order.IsSuccLimitstatement and proof · cited by 255
- Ordinal.typeproof · cited by 207
- IsWellOrderproof · cited by 171
- mul_le_mul_rightproof · cited by 47
- Ordinal.inductionOn₂proof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.isNormal_mul_rightproof · cited by 14
- Ordinal.lt_mul_iff_of_isSuccLimitproof · cited by 1