Description: An atomic lattice with the covering property is a poset. (Contributed by NM, 5-Nov-2012) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | cvlposN | ⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Poset ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvllat | ⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Lat ) | |
2 | latpos | ⊢ ( 𝐾 ∈ Lat → 𝐾 ∈ Poset ) | |
3 | 1 2 | syl | ⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Poset ) |