Testing Blogger's Editor

I am just testing how far the built in blogger   editor can help in laying out proofs. Please ignore  this.


Question: prove distributivity of OR over OR ( I am using "OR" and "AND" for disjunction and conjunction operators , == for equivalence. The reasoning for each step is to the side after a --),

(The calculus used is EQ from "A logical Approach to Discrete Math". This is theorem 3.41, just something chosen at random - but I've used only axioms + theorems proven till that point in the book  ) .



 prove p OR (q OR r) == (p OR q) OR (p OR r)


p OR (q OR r)                                    -- LHS

==   ((p OR q) OR r)                         -- associativity of Or

==  (( p OR q) OR r) OR false          -- False is the identity of OR

==  (( p OR q) OR r) OR (NOT true)   -- definition of false

==   (m or r) OR (NOT true)                 -- substituting m for (p OR q), Leibniz

==   m OR (r OR (NOT true))                -- associativity of OR

==  m OR ( r OR (NOT (p == p)) )         -- true is identity of ==

==  m OR ( r OR ( NOT p == p ))           -- distributivity of NOT over ==

==  m OR (r OR (NOT p) == r  OR p )     -- distributivity of OR over ==  

== m OR (r OR p == r OR (NOT p))        -- symmetry of OR

== (m OR r OR p) == (m OR r OR (NOT p)) -- distributivity of OR over ==

==(p OR q OR r OR p)== (m OR r OR (NOT p)) -- replacing m with (p OR q), Leibniz

==(p OR q) OR (r OR p)== (m OR r OR (NOT p)) --associativity of OR

==(p OR q) OR (p OR r)== (m OR r OR (NOT p)) --symmetry of OR

==(p OR q) OR (p OR r)== (m OR (NOT p) OR r) --symmetry of OR

==(p OR q) OR (p OR r)== (p OR q OR (NOT p) OR r) --expanding m to p OR q, Leibniz

==(p OR q) OR (p OR r)== (p OR (NOT p) OR q OR r) --symmetry of OR

==(p OR q) OR (p OR r)==  ( true OR q OR r)     -- Excluded Middle

== (p OR q) OR (p OR r)==  ( true  OR r)     -- true is the Zero of OR

== (p OR q) OR (p OR r) ==   true      -- true is the Zero of OR

== (p OR q) OR (p OR r)     -- true is the Identity of ==

== RHS . QED



Conclusion: What a mess. I need Latex dammit.  Anyone know of a *non* wordpress blog with a latex plugin? (I don't want JS rendering, for which there are a few options. I want an image (png, gif, jpeg whatever)  generated on the server and plugged in appropriately).