Theorems · Theorem · number theory
Nat.setGcd_dvd_of_mem
∀ {s : Set ℕ} {n : ℕ}, n ∈ s → Nat.setGcd s ∣ n- Defined in
- Mathlib.NumberTheory.FrobeniusNumber
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imageproof · cited by 5,609
- Ideal.spanproof · cited by 948
- Ideal.subset_spanproof · cited by 86
- Nat.setGcdstatement · cited by 15
- Submodule.IsPrincipal.mem_iff_generator_dvdproof · cited by 11
- Int.dvd_natCastproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Nat.setGcd_monoproof · cited by 2
- Nat.setGcd_dvd_of_mem_closureproof · cited by 1
- Nat.exists_mem_span_nat_finset_of_geproof · cited by 1
- Nat.subset_span_setGcdproof · cited by 0
- Nat.setGcd_insert_of_dvdproof · cited by 0