Theorems · Definition · number theory
Nat.setGcd
Set ℕ → ℕ
The gcd of a set of natural numbers is defined to be the nonnegative generator
of the ideal of ℤ generated by them.
- Defined in
- Mathlib.NumberTheory.FrobeniusNumber
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Submodule.IsPrincipal.generatorproof · cited by 56
Cited by15
Results whose statement or proof uses this declaration.
- Nat.setGcd_dvd_of_memstatement · cited by 5
- Nat.dvd_setGcd_iffstatement · cited by 3
- Nat.exists_mem_closure_of_gestatement and proof · cited by 2
- Nat.setGcd_monostatement · cited by 2
- Nat.finite_setOfPred_setGcd_dvd_and_mem_spanstatement and proof · cited by 1
- Nat.exists_mem_span_nat_finset_of_gestatement and proof · cited by 1
- Nat.span_singleton_setGcdstatement · cited by 1
- Nat.exists_ne_zero_of_setGcd_ne_zerostatement and proof · cited by 1
- Nat.setGcd_dvd_of_mem_closurestatement and proof · cited by 1
- Nat.setGcd_eq_zero_iffstatement · cited by 1
- Nat.finite_setOf_setGcd_dvd_and_mem_spanstatement · cited by 0
- exists_frobeniusNumber_iffstatement and proof · cited by 0