Theorems · Theorem · order theory
LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete_of_ne_zero
∀ {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)))- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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- Set.ofPredstatement and proof · cited by 6,101
- Equiv.symmproof · cited by 3,681
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- Units.valproof · cited by 1,966
- map_zeroproof · cited by 1,614
- eq_or_neproof · cited by 1,117
- Multiplicativestatement and proof · cited by 875
- WithZerostatement and proof · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MulEquiv.symmproof · cited by 482
Cited by2
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