theorem Th72:
  (for a holds J,v.(NEx_Val(v,S,x,xSQ)+*(x|a)) |= S) iff for a
  holds J,(v.NEx_Val(v,S,x,xSQ)).(x|a) |= S
proof
  thus (for a holds J,v.(NEx_Val(v,S,x,xSQ)+*(x|a)) |= S) implies for a holds
  J,(v.NEx_Val(v,S,x,xSQ)).(x|a) |= S
  proof
    assume
A1: for a holds J,v.(NEx_Val(v,S,x,xSQ)+*(x|a)) |= S;
    let a;
    v.(NEx_Val(v,S,x,xSQ)+*(x|a)) = (v.NEx_Val(v,S,x,xSQ)).(x|a) by FUNCT_4:14;
    hence thesis by A1;
  end;
  thus (for a holds J,(v.NEx_Val(v,S,x,xSQ)).(x|a) |= S) implies for a holds J
  ,v.(NEx_Val(v,S,x,xSQ)+*(x|a)) |= S
  proof
    assume
A2: for a holds J,(v.NEx_Val(v,S,x,xSQ)).(x|a) |= S;
    let a;
    v.(NEx_Val(v,S,x,xSQ)+*(x|a)) = (v.NEx_Val(v,S,x,xSQ)).(x|a) by FUNCT_4:14;
    hence thesis by A2;
  end;
end;
