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<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> holds  <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="equation.html#K1" title="EQUATION:func.1">""</a> <font color="Olive" title="b1">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="equation.html#K1" title="EQUATION:func.1">""</a> <font color="Maroon" title="c2">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">A</font></span><br/>



<a NAME="E1:17"/>
 <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">A</font> is <a href="msualg_3.html#V2" title="MSUALG_3:attr.2">"onto"</a>
 
<b>by </b><i><a class="ref" href="autalg_1.html#T24" title="AUTALG_1:th.24">AUTALG_1:24</a></i>;<br/>
<a NAME="E2:17"/><b>then </b><i><font color="Green" title="E8">A1</font></i>: 
 <a href="mssubfam.html#K2" title="MSSUBFAM:func.2">rngs</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="extens_1.html#T13" title="EXTENS_1:th.13">EXTENS_1:13</a></i>;<br/>
<a NAME="E3:17"/>
 <a href="mssubfam.html#K1" title="MSSUBFAM:func.1">doms</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T17" title="MSSUBFAM:th.17">MSSUBFAM:17</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
<span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="equation.html#K1" title="EQUATION:func.1">""</a> <font color="Maroon" title="c2">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="equation.html#E2:17"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="equation.html#T15" target="_self" title="EQUATION:th.15">Th15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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