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<b>let </b><font color="Maroon" title="c1">X</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">l2</font>, <font color="Olive" title="b2">l1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K5" title="COH_SP:func.5">MapsC</a> <font color="Maroon" title="c1">X</font>  st  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Olive" title="b1">l2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Olive" title="b2">l1</font> holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b1">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Olive" title="b2">l1</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">l2</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">l1</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Olive" title="b2">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Olive" title="b2">l1</font> &amp;  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Olive" title="b2">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Olive" title="b1">l2</font> )</span><br/><b>let </b><font color="Maroon" title="c2">l2</font>, <font color="Maroon" title="c3">l1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K5" title="COH_SP:func.5">MapsC</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c3">l1</font> implies ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l1</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c3">l1</font> &amp;  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l2</font> ) )</span><br/>





<b>assume </b><a NAME="E1:39"/>
 <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c2">l2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c3">l1</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"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l1</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c3">l1</font> &amp;  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l2</font> )</span><br/>

<b>then </b><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c3">l1</font></span>)</span>,<span class="p3">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">l1</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> = 
<font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font>
<b>by </b><i><a class="ref" href="coh_sp.html#D13" target="_self" title="COH_SP:def.13">Def13</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="coh_sp.html#T20" target="_self" title="COH_SP:th.20">Th20</a></i>
;<br/>
<b>hence </b><a NAME="E3:39"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">l1</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K6" title="COH_SP:func.6">dom</a> <font color="Maroon" title="c3">l1</font> &amp;  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="coh_sp.html#K9" title="COH_SP:func.9">*</a> <font color="Maroon" title="c3">l1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K7" title="COH_SP:func.7">cod</a> <font color="Maroon" title="c2">l2</font> )
 <b>by </b><i><a class="txt" href="coh_sp.html#E34"><i><font color="Green" title="E16">Lm2</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</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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