Theorems · Theorem · number theory
Nat.setGcd_dvd_of_mem_closure
∀ {s : Set ℕ} {n : ℕ}, n ∈ AddSubmonoid.closure s → Nat.setGcd s ∣ n- Defined in
- Mathlib.NumberTheory.FrobeniusNumber
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- dvd_zeroproof · cited by 63
- AddSubmonoid.closure_inductionproof · cited by 30
- dvd_addproof · cited by 25
- Nat.setGcdstatement and proof · cited by 15
- Nat.setGcd_dvd_of_memproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- exists_frobeniusNumber_iffproof · cited by 0