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<span class="kw">let </span><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 23 &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 365 implies  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 )</span><br/>

<span class="kw">assume </span><a NAME="E1:29"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 23
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 365 or  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 )</span><br/>

<span class="kw">assume </span><a NAME="E2:29"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 365
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">E</font> =  <a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c6">comega</font> =  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span>;<br/>
<a NAME="E3:29"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p3">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cardfin2.html#T17" target="_self" onmouseover="rs('cardfin2/T17')" onmouseout="rh()">Th17</a>, <a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="xreal_1.html#T74" onmouseover="rs('xreal_1/T74')" onmouseout="rh()">XREAL_1:74</a></span>;<br/>
<a NAME="E4:29"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T74" onmouseover="rs('xreal_1/T74')" onmouseout="rh()">XREAL_1:74</a></span>;<br/>
<a NAME="E5:29"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p3">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
;<br/>
<a NAME="E6:29"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D7" onmouseover="rs('xcmplx_0/D7')" onmouseout="rh()">XCMPLX_0:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:29"/>
 <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><a href="cardfin2.html#K4" title="CARDFIN2:func.4">not-one-to-one</a> (<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rpr_1.html#D1" onmouseover="rs('rpr_1/D1')" onmouseout="rh()">RPR_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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