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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.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/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E1:18"/>
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="autalg_1.html#T24" title="AUTALG_1:th.24">AUTALG_1:24</a></span>;<br/>
<a NAME="E2:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 <a href="funct_6.html#K3" title="FUNCT_6:func.3">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extens_1.html#T13" title="EXTENS_1:th.13">EXTENS_1:13</a></span>;<br/>
<a NAME="E3:18"/>
 <a href="funct_6.html#K2" title="FUNCT_6:func.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mssubfam.html#T17" title="MSSUBFAM:th.17">MSSUBFAM:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:18"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="equation.html#T15" target="_self" title="EQUATION:th.15">Th15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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