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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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">f</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/> for <font color="Olive" title="b2">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds  <font color="Olive" title="b2">d</font> <a href="rfunct_3.html#R1" title="RFUNCT_3:pred.1">is_common_for_dom</a>  <a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">D</font></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds  <font color="Olive" title="b1">d</font> <a href="rfunct_3.html#R1" title="RFUNCT_3:pred.1">is_common_for_dom</a>  <a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span><br/><b>let </b><font color="Maroon" title="c3">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">d</font> <a href="rfunct_3.html#R1" title="RFUNCT_3:pred.1">is_common_for_dom</a>  <a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span><br/><b>let </b><font color="Maroon" title="c4">G</font> be    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="rfunct_3.html#D9" target="_self" title="RFUNCT_3:def.9">RFUNCT_3:def 9</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">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> holds <br/><font color="Maroon" title="c3">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">G</font></span><br/><b>let </b><font color="Maroon" title="c5">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> implies <font color="Maroon" title="c3">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">G</font> )</span><br/>









<b>assume </b><a NAME="E1:48"/>
( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">G</font></span><br/>

<a NAME="E2:48"/><b>then </b>
<font color="Maroon" title="c4">G</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rfunct_1.html#K5" title="RFUNCT_1:func.5">chi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span>,<font color="Maroon" title="c1">D</font>
 
<b>by </b><i><a class="ref" href="rfunct_3.html#D6" target="_self" title="RFUNCT_3:def.6">Def6</a></i>;<br/>
<a NAME="E3:48"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T77" title="RFUNCT_1:th.77">RFUNCT_1:77</a></i>;<br/>
<b>hence </b><a NAME="E4:48"/>
<font color="Maroon" title="c3">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">G</font>
 ; <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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