Re: Proof of Completeness of Algebraic Properties of Relational Lattice
From: Mikito Harakiri <mikharakiri_nospaum_at_yahoo.com>
Date: 24 May 2006 10:00:25 -0700
Message-ID: <1148490025.153620.203650_at_i40g2000cwc.googlegroups.com>
Date: 24 May 2006 10:00:25 -0700
Message-ID: <1148490025.153620.203650_at_i40g2000cwc.googlegroups.com>
Vadim Tropashko wrote:
> Existence of distributor hinges on the following
> inequality:
>
>
> A /\ (B \/ C) >= (A /\ B) \/ (A /\ C)
This identity is true in any lattice, not only relational one. Hence it can be proved witut need to invoke distributivity criteria.
- A /\ (B \/ C) >= (A /\ B)
Proof: A /\ (B \/ C) /\ (A /\ B) = A /\ B /\ (B \/ C) = A /\ B
2. A /\ (B \/ C) >= (A /\ C)
3. A /\ (B \/ C) >= (A /\ B) \/ (A /\ C) Received on Wed May 24 2006 - 19:00:25 CEST