Theorems · Definition · number theory
PNat.equivNonZeroDivisorsNat
ℕ+ ≃*o ↥(nonZeroDivisors ℕ)
ℕ+ is equivalent to nonZeroDivisors ℕ in terms of order and multiplication.
- Defined in
- Mathlib.Algebra.Order.Monoid.PNat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- PNatstatement and proof · cited by 392
- PNat.valproof · cited by 226
- OrderMonoidIsostatement · cited by 114
Cited by9
Results whose statement or proof uses this declaration.
- DivisibleHull.mkproof · cited by 19
- DivisibleHull.mk_zeroproof · cited by 2
- DivisibleHull.liftOnproof · cited by 2
- DivisibleHull.nnqsmul_mkproof · cited by 1
- DivisibleHull.liftOn₂proof · cited by 1
- DivisibleHull.mk_eq_mkproof · cited by 1
- DivisibleHull.indproof · cited by 0
- PNat.equivNonZeroDivisorsNat_apply_coestatement and proof · cited by 0
- PNat.equivNonZeroDivisorsNat_symm_apply_coestatement and proof · cited by 0