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<b>let </b><font color="Maroon" title="c2">h1</font>, <font color="Maroon" title="c3">h2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font>, <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"> ( ( for <font color="Olive" title="b1">C</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c2">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <font color="Olive" title="b1">C</font> ) &amp; ( for <font color="Olive" title="b1">C</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c3">h2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <font color="Olive" title="b1">C</font> ) implies <font color="Maroon" title="c2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:43_4_2"/><i><font color="Green" title="E23">A19</font></i>: 
for <font color="Olive" title="b1">C</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c2">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <font color="Olive" title="b1">C</font>
 <b>and </b><br/><a NAME="E2:43_4_2"/><i><font color="Green" title="E24">A20</font></i>: 
for <font color="Olive" title="b1">C</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c3">h2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <font color="Olive" title="b1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_4_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">C</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</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"> <font color="Maroon" title="c2">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">C</font></span><br/><b>thus </b><font color="Maroon" title="c2">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">C</font> = 
 <a href="coh_sp.html#K8" title="COH_SP:func.8">id$</a> <font color="Maroon" title="c4">C</font>
<b>by </b><i><a class="txt" href="coh_sp.html#E1:43_4_2"><i><font color="Green" title="E23">A19</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">h2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">C</font>
<b>by </b><i><a class="txt" href="coh_sp.html#E2:43_4_2"><i><font color="Green" title="E24">A20</font></i></a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:43_4_2"/>
<font color="Maroon" title="c2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</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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