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<b>let </b><font color="Maroon" title="c5">T1</font>, <font color="Maroon" title="c6">T2</font> be   <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c3">S</font>,<span class="p1">(<span class="default"><a href="group_10.html#K3" title="GROUP_10:func.3">the_subsets_of_card</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">E</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:15_1_2"/><i><font color="Green" title="E8">A14</font></i>: 
for <font color="Olive" title="b1">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> holds  <font color="Maroon" title="c5">T1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#K4" title="GROUP_10:func.4">the_extension_of_left_translation_of</a> <font color="Maroon" title="c2">n</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">LO</font>
 <b>and </b><br/><a NAME="E2:15_1_2"/><i><font color="Green" title="E9">A15</font></i>: 
for <font color="Olive" title="b1">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> holds  <font color="Maroon" title="c6">T2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#K4" title="GROUP_10:func.4">the_extension_of_left_translation_of</a> <font color="Maroon" title="c2">n</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">LO</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:15_1_2_1"/>
<font color="Maroon" title="c7">x</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 <font color="Maroon" title="c3">S</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c8">s</font> = <font color="Maroon" title="c7">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> ;<br/><b>thus </b><font color="Maroon" title="c5">T1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
 <a href="group_10.html#K4" title="GROUP_10:func.4">the_extension_of_left_translation_of</a> <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c8">s</font>,<font color="Maroon" title="c4">LO</font>
<b>by </b><i><a class="txt" href="group_10.html#E1:15_1_2"><i><font color="Green" title="E8">A14</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">T2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="group_10.html#E2:15_1_2"><i><font color="Green" title="E9">A15</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_2"/>
<font color="Maroon" title="c5">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">T2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>;<br/>


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