Theorems · Theorem · order theory
LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_ge_gt_iff_nonempty_discrete_of_ne_zero
∀ {G₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero G₀] [Nontrivial G₀ˣ] {g : G₀},
g ≠ 0 → (({x | x ≤ g}.WellFoundedOn fun x1 x2 => x1 > x2) ↔ Nonempty (G₀ ≃*o WithZero (Multiplicative ℤ)))- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- eq_or_neproof · cited by 1,117
- Multiplicativestatement · cited by 875
- WithZerostatement · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- inv_zeroproof · cited by 184
- OrderMonoidIsostatement · cited by 114
- Set.WellFoundedOnstatement and proof · cited by 53
- inv_anti₀proof · cited by 27
- inv_strictAnti₀proof · cited by 10
Cited by2
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