
theorem
  and2.<*0,0*>=0 & and2.<*0,1*>=0 & and2.<*1,0*>=0 & and2.<*1,1*>=1 &
and2a.<*0,0*>=0 & and2a.<*0,1*>=1 & and2a.<*1,0*>=0 & and2a.<*1,1*>=0 & nor2.
  <*0,0*>=1 & nor2.<*0,1*>=0 & nor2.<*1,0*>=0 & nor2.<*1,1*>=0
proof
  thus and2.<*0,0*> = FALSE '&' FALSE by FACIRC_1:def 6
    .= 0;
  thus and2.<*0,1*> = FALSE '&' TRUE by FACIRC_1:def 6
    .= 0;
  thus and2.<*1,0*> = TRUE '&' FALSE by FACIRC_1:def 6
    .= 0;
  thus and2.<*1,1*> = TRUE '&' TRUE by FACIRC_1:def 6
    .= 1;
  thus and2a.<*0,0*> = 'not' FALSE '&' FALSE by Def1
    .= 0;
  thus and2a.<*0,1*> = 'not' FALSE '&' TRUE by Def1
    .= 1;
  thus and2a.<*1,0*> = 'not' TRUE '&' FALSE by Def1
    .= 0;
  thus and2a.<*1,1*> = 'not' TRUE '&' TRUE by Def1
    .= 0;
  thus nor2.<*0,0*> = TRUE '&' 'not' FALSE by Lm3
    .= 1;
  thus nor2.<*0,1*> = 'not' FALSE '&' 'not' TRUE by Lm3
    .= 0;
  thus nor2.<*1,0*> = 'not' TRUE '&' 'not' FALSE by Lm3
    .= 0;
  thus nor2.<*1,1*> = FALSE '&' 'not' TRUE by Lm3
    .= 0;
end;
