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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="144_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:144_1_1_1"/>
( <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or  not <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="144_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:144_1_1_1_1"/>
<font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c2">f</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/><div class="add"><a NAME="E2:144_1_1_1_1"/><span class="kw">then </span>
 <a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/><a NAME="E3:144_1_1_1_1"/><span class="kw">then </span>
 <a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_5.html#T64" title="FUNCT_5:th.64">FUNCT_5:64</a></span>;<br/><span class="kw">hence </span><a NAME="E4:144_1_1_1_1"/>
 <a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c2">f</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="144_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:144_1_1_1_2"/>
not <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c2">f</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">X</font> = <font color="Maroon" title="c1">X</font> as  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>  ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c2">f</font> as   <a href="pre_poly.html#V2" title="PRE_POLY:attr.2">finite-support</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">X</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><a NAME="E4:144_1_1_1_2"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K48" title="BINOP_2:func.48">multnat</a>  <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K20" title="PRE_POLY:func.20">support</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> <font color="Maroon" title="c4">f</font>,1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T63" target="_self" title="PRE_POLY:th.63">Th67</a></span>;<br/><span class="kw">hence </span><a NAME="E5:144_1_1_1_2"/>
 <a href="pre_poly.html#K19" title="PRE_POLY:func.19">NatMinor</a> <font color="Maroon" title="c2">f</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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