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Theorems · Theorem · group theory

Submonoid.mem_pos

∀ {α : Type u_1} [inst : MulZeroOneClass α] [inst_1 : PartialOrder α] [inst_2 : PosMulStrictMono α]
  [inst_3 : ZeroLEOneClass α] [inst_4 : NeZero 1] {a : α}, a ∈ Submonoid.pos α ↔ 0 < a
Defined in
Mathlib.Algebra.Order.GroupWithZero.Submonoid
Cited by
0 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
MulZeroOneClassPartialOrderPosMulStrictMonoZeroLEOneClassNeZero
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Around this declaration

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PartialOrder · cited by 6410PartialOrderSubmonoid · cited by 3086SubmonoidZeroLEOneClass · cited by 304ZeroLEOneClassMulZeroOneClass · cited by 184MulZeroOneClassPosMulStrictMono · cited by 151PosMulStrictMonoSubmonoid.pos · cited by 3Submonoid.posSubmonoid.mem_posCITED BYCITES

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