<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font>, <font color="Maroon" title="c5">h</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>let </b><font color="Maroon" title="c6">F</font> be   <a href="group_7.html#NM1" title="GROUP_7:NM.1">HGrStr-Family</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c7">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> ;<br/><b>let </b><font color="Maroon" title="c8">p</font>, <font color="Maroon" title="c9">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c6">F</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c10">x</font>, <font color="Maroon" title="c11">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">G</font>;<br/>

















<b>assume </b><b>that </b><br/><a NAME="E1:11"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 <b>and </b><br/><a NAME="E2:11"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c7">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font>
 <b>and </b><br/><a NAME="E3:11"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font> &amp; <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">q</font> )
 <b>and </b><br/><a NAME="E4:11"/><i><font color="Green" title="E8">A4</font></i>: 
( <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x</font> &amp; <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">y</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c12">GP</font> =  <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c6">F</font>;<br/>
<a NAME="E5:11"/>
( <font color="Maroon" title="c8">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c6">F</font></span>)</span> &amp; <font color="Maroon" title="c9">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c6">F</font></span>)</span> )
 
;<br/>
<a NAME="E6:11"/><b>then </b>
( <font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c6">F</font></span>)</span> &amp; <font color="Maroon" title="c4">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c6">F</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="group_7.html#E3:11"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="group_7.html#D2" target="_self" title="GROUP_7:def.2">Def2</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">Fi</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> , <font color="Maroon" title="c14">m</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E8:11"/><i><font color="Green" title="E9">A5</font></i>: 
( <font color="Maroon" title="c13">Fi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Maroon" title="c14">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> &amp; <font color="Maroon" title="c14">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c13">Fi</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font></span>)</span> )
 <b>by </b><i><a class="txt" href="group_7.html#E1:11"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="group_7.html#D2" target="_self" title="GROUP_7:def.2">Def2</a></i>;<br/>
<b>thus </b><a NAME="E9:11"/>
<font color="Maroon" title="c10">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font>
 <b>by </b><i><a class="txt" href="group_7.html#E2:11"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="group_7.html#E3:11"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="group_7.html#E4:11"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="group_7.html#E8:11"><i><font color="Green" title="E9">A5</font></i></a></i>;<br/>


</div>
