Some LaTeX commands

\Moreover

Cycling through Moreover, Furthermore, In addition and Next

The following code defines the command \Moreover, which expands to one of the following, cycling through the options:

Moreover, we note/observe that
Furthermore, we note/observe that
In addition, we note/observe that
Next we note/observe that

Code for the \Moreover command

\ExplSyntaxOn

\int_new:N \g_furthermore

\NewDocumentCommand{\Moreover}{ o o }{
  \IfValueT{#1}{
    \str_case:nn {#1} {
      {Next} {\int_gset:Nn {\g_furthermore} {0}}      
      {Furthermore} {\int_gset:Nn {\g_furthermore} {1}}
      {Moreover} {\int_gset:Nn {\g_furthermore} {2}}
      {In~addition} {\int_gset:Nn {\g_furthermore} {3}}
      {note} {\bool_gset_true:N \g_noteobserve}
      {observe} {\bool_gset_false:N \g_noteobserve}
    }
    \IfValueT{#2}{
      \str_case:nn {#2} {
        {Next} {\int_gset:Nn {\g_furthermore} {0}}        
        {Furthermore} {\int_gset:Nn {\g_furthermore} {1}}
        {Moreover} {\int_gset:Nn {\g_furthermore} {2}}
        {In~addition} {\int_gset:Nn {\g_furthermore} {3}}
        {note} {\bool_gset_true:N \g_noteobserve}
        {observe} {\bool_gset_false:N \g_noteobserve}
      }
    }
  }
  \int_case:nn { \int_mod:nn {\g_furthermore} {4} } {
    { 0 } { Next~\nobs that}    
    { 1 } { Furthermore,~\nobs that}
    { 2 } { Moreover,~\nobs that}
    { 3 } { In~addition,~\nobs that}
  }
  \int_incr:N \g_furthermore
  \peek_charcode:NTF , {  } { ~ }
}

\ExplSyntaxOff

The command takes up to two optional arguments which can take the values Next, Furthermore, Moreover, In addition, note, or observe and forces the command to use the corresponding expression. This can be used, e.g., if a particularly short or long expression is desired to avoid overfull hboxes.

Here is an example that shows how this command works:

\Moreover the fact that $a>0$ implies that $a^3>0$. 
\Moreover the fact that $b\leq 1$ ensures that $2b\leq 2$. 
\Moreover[Next] the asumption that $n$ is even shows that $3n$ is even.
\Moreover[In addition][note] the assumption that $f\in C^1(\R,\R)$ shows that $f$ is continuous.

Next note that the fact that $a>0$ implies that $a^3>0$. Furthermore, observe that the fact that $b\leq 1$ ensures that $2b\leq 2$. Next note that the asumption that $n$ is even shows that $3n$ is even. In addition, note that the assumption that $f\in C^1(\mathbb R,\mathbb R)$ shows that $f$ is continuous.