Theorems · Theorem · commutative algebra
Prime.not_dvd_lcm
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] {a b p : α},
Prime p → ¬p ∣ a → ¬p ∣ b → ¬p ∣ lcm a b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Iff.notproof · cited by 489
- Primestatement and proof · cited by 277
- GCDMonoidstatement and proof · cited by 96
- GCDMonoid.lcmstatement · cited by 78
- Prime.dvd_lcmproof · cited by 1
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