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<span class="kw">set </span><font color="Maroon" title="c4">gf</font> = <font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">X</font> = <font color="Maroon" title="c3">x</font> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T1" onmouseover="rs('tarski/T1')" onmouseout="rh()">TARSKI:1</a></span>;<br/>
<a NAME="E2:68_2_1"/><span class="lab"><font color="Green" title="E39">A5</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D6" onmouseover="rs('fomodel2/D6')" onmouseout="rh()">FOMODEL2:def 6</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_2_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:68_2_1_1"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> or  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:68_2_1_1_1"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c3">x</font></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> </span><br/><div class="add"><a NAME="E2:68_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68_2_1"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="fomodel2.html#D6" onmouseover="rs('fomodel2/D6')" onmouseout="rh()">FOMODEL2:def 6</a></span>;<br/><a NAME="E3:68_2_1_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68_2_1_1_1"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="txt" href="#E2:68_2_1"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">fx</font> = <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">X</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">g</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" onmouseover="rs('finseq_1/D11')" onmouseout="rh()">FINSEQ_1:def 11</a></span>;<br/><a NAME="E5:68_2_1_1_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c6">fx</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">g</font>
 ;<br/><a NAME="E6:68_2_1_1_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">fx</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</a>, <a class="txt" href="#E2:68_2_1_1_1"><span class="lab"><font color="Green" title="E41">A7</font></span></a></span>;<br/><a NAME="E7:68_2_1_1_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">fx</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/><span class="kw">hence </span><a NAME="E8:68_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c3">x</font></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:68_2_1_1_2"/>
 not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c3">x</font></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> </span><br/><div class="add"><a NAME="E2:68_2_1_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68_2_1"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:68_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="flexary1.html#NK6" title="FLEXARY1:NK.6">*.</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c3">x</font></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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