Theorems · Theorem · order theory
LinearOrderedCommGroup.wellFoundedOn_setOfPred_ge_gt_iff_nonempty_discrete
∀ {G : Type u_2} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] [Nontrivial G] (g : G),
({x | x ≤ g}.WellFoundedOn fun x1 x2 => x1 > x2) ↔ Nonempty (G ≃*o Multiplicative ℤ)- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.ofPredstatement and proof · cited by 6,101
- Nontrivialstatement and proof · cited by 2,416
- CommGroupstatement and proof · cited by 990
- Multiplicativestatement · cited by 875
- IsOrderedMonoidstatement and proof · cited by 577
- OrderMonoidIsostatement · cited by 114
- Set.WellFoundedOnstatement and proof · cited by 53
- Set.WellFoundedOn.mapsToproof · cited by 7
- Set.WellFoundedOn.mono'proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discreteproof · cited by 0