Theorems · Theorem · order theory
LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero
Deprecated since 2026-07-09Use LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete_of_ne_zero instead.
∀ {G₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero G₀] [Nontrivial G₀ˣ] {g : G₀},
g ≠ 0 → (({x | g ≤ x}.WellFoundedOn fun x1 x2 => x1 < x2) ↔ Nonempty (G₀ ≃*o WithZero (Multiplicative ℤ)))Alias of LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete_of_ne_zero.
- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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- Set.ofPredstatement · cited by 6,101
- Unitsstatement · cited by 2,804
- Nontrivialstatement · cited by 2,416
- Multiplicativestatement · cited by 875
- WithZerostatement · cited by 586
- LinearOrderedCommGroupWithZerostatement · cited by 528
- OrderMonoidIsostatement · cited by 114
- Set.WellFoundedOnstatement · cited by 53
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