Theorems · Theorem · logic and foundations
Ordinal.mul_div_gc
∀ {a : Ordinal.{u_4}}, a ≠ 0 → GaloisConnection (fun x => a * x) fun x => x / aMultiplication and division by a non-zero ordinal form a Galois connection.
- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- Ordinalstatement and proof · cited by 1,688
- Set.Iicproof · cited by 1,111
- GaloisConnectionstatement · cited by 253
- Ne.posproof · cited by 17
- Ordinal.isNormal_mul_rightproof · cited by 14
- Order.IsNormal.le_iff_le_sSup'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.mul_le_iff_le_divproof · cited by 10
- Ordinal.lt_mul_iff_div_ltproof · cited by 8