Theorems · Theorem · order theory
LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete
Deprecated since 2026-07-09Use LinearOrderedCommGroup.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete instead.
∀ {G : Type u_2} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] [Nontrivial G] {g : G},
({x | g ≤ x}.WellFoundedOn fun x1 x2 => x1 < x2) ↔ Nonempty (G ≃*o Multiplicative ℤ)Alias of LinearOrderedCommGroup.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete.
- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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- LinearOrderstatement · cited by 8,572
- Set.ofPredstatement · cited by 6,101
- Nontrivialstatement · cited by 2,416
- CommGroupstatement · cited by 990
- Multiplicativestatement · cited by 875
- IsOrderedMonoidstatement · cited by 577
- OrderMonoidIsostatement · cited by 114
- Set.WellFoundedOnstatement · cited by 53
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