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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a> holds   <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">q</font> =  <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>;<br/>
<span class="lab"><font color="Green" title="E69">A</font></span>: <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T75" title="AFINSQ_1:th.75">AFINSQ_1:75</a></span>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T34" title="NAT_D:th.34">NAT_D:34</a></span>
;<br/>
<span class="lab"><font color="Green" title="E70">B</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> = 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T75" title="AFINSQ_1:th.75">AFINSQ_1:75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T2" title="AFINSQ_1:th.2">AFINSQ_1:2</a></span>
;<br/>
<a NAME="E3:120"/><span class="lab"><font color="Green" title="E71">C</font></span>: 
 not  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 
;<br/>
<a NAME="E4:120"/>
 <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><span class="lab"><font color="Green" title="E72">K</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:120"><span class="lab"><font color="Green" title="E69">A</font></span></a>, <a class="ref" href="valued_1.html#T36" title="VALUED_1:th.36">VALUED_1:36</a></span>
<br/>.= 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:120"><span class="lab"><font color="Green" title="E70">B</font></span></a>, <a class="txt" href="#E3:120"><span class="lab"><font color="Green" title="E71">C</font></span></a>, <a class="ref" href="zfmisc_1.html#T117" title="ZFMISC_1:th.117">ZFMISC_1:117</a></span>
;<br/> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_1.html#D11" title="FUNCT_1:def.11">FUNCT_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> or <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> or <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E6:120"/><span class="lab"><font color="Green" title="E73">Z</font></span>: 
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font></span><br/>

<a NAME="E7:120"/><span class="lab"><font color="Green" title="E74">D</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/>
<a NAME="E8:120"/>
 <a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="valued_1.html#K63" title="VALUED_1:func.63">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:120"><span class="lab"><font color="Green" title="E73">Z</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:120"><span class="lab"><font color="Green" title="E73">Z</font></span></a>, <a class="txt" href="#E5:120"><span class="lab"><font color="Green" title="E72">K</font></span></a>, <a class="txt" href="#E7:120"><span class="lab"><font color="Green" title="E74">D</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
