Theorems · Theorem · commutative algebra
nonempty_normalizedGCDMonoid_iff_isGCDMonoid
∀ {α : Type u_2} [inst : CommMonoidWithZero α], Nonempty (NormalizedGCDMonoid α) ↔ IsGCDMonoid α- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizationMonoidproof · cited by 165
- Classical.arbitraryproof · cited by 161
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdproof · cited by 143
- GCDMonoidproof · cited by 96
- IsGCDMonoidstatement and proof · cited by 12
- dvd_gcd_iffproof · cited by 8
- normalizedGCDMonoidOfExistsGCDproof · cited by 1
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