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<b>let </b><font color="Maroon">a</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">c</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">d</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>given </b><font color="Maroon">x</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><a NAME="E1:6"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a><br/>

<b>given </b><font color="Maroon">y</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><a NAME="E2:6"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a><br/>

<b>take </b>
<font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a><br/>

<b>thus </b><a NAME="E3:6"/>
<font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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