Theorems · Theorem · logic and foundations
exists_wellFoundedGT
∀ (α : Type u), ∃ x, WellFoundedGT α
The well-ordering theorem (or Zermelo's theorem): every type can be co-well-ordered.
- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement · cited by 8,572
- Function.swapproof · cited by 216
- WellFoundedGTstatement · cited by 114
- IsWellFounded.wfproof · cited by 43
- WellOrderingRelproof · cited by 30
- linearOrderOfSTOproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_mul_of_isDomainproof · cited by 3