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<b>let </b><font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M2" target="_self">SubStr</a> of  <a href="monoid_0.html#K7" target="_self">&lt;REAL,*&gt;</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>;<br/>



<a NAME="E1:117"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">N</font>) <a href="tarski.html#R1">c=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K7" target="_self">&lt;REAL,*&gt;</a> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="monoid_0.html#K7" target="_self">&lt;REAL,*&gt;</a>  <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:117"/>
<font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b'</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:117"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> holds <br/><font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> <a href="binop_2.html#K11">*</a> <font color="Olive">y</font>
 <b>by </b><i/>;<br/>


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