Description: Hilbert lattice join is the least upper bound of two elements. (Contributed by NM, 11-Jun-2004) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ch0le.1 | |- A e. CH |
|
chjcl.2 | |- B e. CH |
||
chlub.1 | |- C e. CH |
||
Assertion | chlubi | |- ( ( A C_ C /\ B C_ C ) <-> ( A vH B ) C_ C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ch0le.1 | |- A e. CH |
|
2 | chjcl.2 | |- B e. CH |
|
3 | chlub.1 | |- C e. CH |
|
4 | 1 | chshii | |- A e. SH |
5 | 2 | chshii | |- B e. SH |
6 | 4 5 3 | shlubi | |- ( ( A C_ C /\ B C_ C ) <-> ( A vH B ) C_ C ) |