Theorems · Theorem · order theory
Subgroup.isLeast_of_closure_iff_eq_mabs
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] [MulArchimedean G] {a b : G},
IsLeast {y | y ∈ Subgroup.closure {a} ∧ 1 < y} b ↔ b = |a|ₘ ∧ 1 < b- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- Subgroupstatement · cited by 3,593
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
- CommGroupstatement and proof · cited by 990
- pow_oneproof · cited by 894
- IsOrderedMonoidstatement and proof · cited by 577
- inv_invproof · cited by 494
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