The prior of (5) is proved. The after is similar. Having

Having( a , a )( a , a ),( a , a )( a , a )( b , b ),then ( a , a )( a , a )Λ( ( a , a )( b , b ) )( a , a );thus, ( a , a )Λ( ( a , a )( b , b ) )=( a , a ). Corollaries:( a , a )Λ( ( a , a )Λ( b , b ) )=( a , a )

Definition 8.22 We call partial order set ( ( L , L ), ) semilattice; when ( α , α ), ( β , β )( L , L ),wehave( α , α )( β

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