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<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funcop_1.html#D6" onmouseover="rs('funcop_1/D6')" onmouseout="rh()">FUNCOP_1:def 6</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"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <span class="p1">(<span class="default"><a href="idea_1.html#K18" title="IDEA_1:func.18">IDEA_Q_F</a> (<font color="Maroon" title="c4">Key</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c1">r</font>)</span>)</span> or <span class="p1">(<span class="default"><a href="idea_1.html#K18" title="IDEA_1:func.18">IDEA_Q_F</a> (<font color="Maroon" title="c4">Key</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c1">r</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:55_1_1"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="idea_1.html#K18" title="IDEA_1:func.18">IDEA_Q_F</a> (<font color="Maroon" title="c4">Key</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c1">r</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"><a href="idea_1.html#K18" title="IDEA_1:func.18">IDEA_Q_F</a> (<font color="Maroon" title="c4">Key</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c1">r</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">xx</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:55_1_1"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c6">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 ;<br/>
<a NAME="E4:55_1_1"/>
<span class="p1">(<span class="default"><a href="idea_1.html#K18" title="IDEA_1:func.18">IDEA_Q_F</a> (<font color="Maroon" title="c4">Key</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c1">r</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">xx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K16" title="IDEA_1:func.16">IDEA_Q</a> (<span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c4">Key</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c6">xx</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>,<font color="Maroon" title="c3">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55_1_1"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55_1_1"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="idea_1.html#D18" target="_self" onmouseover="rs('idea_1/D18')" onmouseout="rh()">Def18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:55_1_1"/>
<span class="p1">(<span class="default"><a href="idea_1.html#K18" title="IDEA_1:func.18">IDEA_Q_F</a> (<font color="Maroon" title="c4">Key</font>,<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c1">r</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:55_1_1"><span class="lab"><font color="Green" title="E43">A2</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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