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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span>$1 is   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E2:75_1_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<font color="Maroon" title="c1">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="xboole_0.html#S1" onmouseover="rs('xboole_0/S1')" onmouseout="rh()">XBOOLE_0:sch 1</a>();<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c2">X</font>
; <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">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff <font color="Olive" title="b1">x</font> is   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff <font color="Maroon" title="c3">x</font> is   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:75_1_1"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c3">x</font> is   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></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"> ( <font color="Maroon" title="c3">x</font> is   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font> implies <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:75_1_1"/>
<font color="Maroon" title="c3">x</font> is   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font>
 ; <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"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c3">x</font> as   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">p</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<font color="Maroon" title="c1">D</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T12" target="_self" onmouseover="rs('afinsq_1/T12')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E7:75_1_1"/>
<font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<font color="Maroon" title="c1">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
;<br/>
<span class="kw">hence </span><a NAME="E8:75_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></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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