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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">m2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K21" target="_self">MapsT</a> <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K21" target="_self">MapsT</a> <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:74"/>
 <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m1</font>
 ;<br/>

<b>then </b><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m1</font></span>)</span>,<span class="p3">(<span class="default"><a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m2</font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> = 
<font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font>
<b>by </b><i><a class="ref" href="coh_sp.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><a href="coh_sp.html#K22" target="_self">dom</a> <span class="p4">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="coh_sp.html#K23" target="_self">cod</a> <span class="p4">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:74"/>
( <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K22" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K22" target="_self">dom</a> <font color="Maroon">m1</font> &amp;  <a href="coh_sp.html#K23" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="coh_sp.html#K25" target="_self">*</a> <font color="Maroon">m1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K23" target="_self">cod</a> <font color="Maroon">m2</font> )
 <b>by </b><i><a class="ref" href="coh_sp.html#D2" target="_self">Def2</a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>


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