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<span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of 8 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default">6 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></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"> ( <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<font color="Maroon" title="c1">r</font>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,6)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,12)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,18)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,24)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,30)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,36)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,42) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<font color="Maroon" title="c1">r</font>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,6)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,12)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,18)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,24)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,30)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,36)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,42) implies <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:74_1_2"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
( <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<font color="Maroon" title="c1">r</font>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,6)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,12)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,18)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,24)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,30)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,36)</span>)</span>,6) &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,42) )
 ; <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="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<font color="Maroon" title="c1">r</font>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,6)</span>)</span>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,12)</span>)</span>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,18)</span>)</span>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,24)</span>)</span>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,30)</span>)</span>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,36)</span>)</span>,6) or  not <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,42) or <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:74_1_2"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
( <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<font color="Maroon" title="c1">r</font>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,6)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,12)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,18)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,24)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,30)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K2" title="DESCIP_1:func.2">Op-Left</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,36)</span>)</span>,6) &amp; <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="descip_1.html#K3" title="DESCIP_1:func.3">Op-Right</a> (<font color="Maroon" title="c1">r</font>,42) )
 ; <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="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font></span><br/>

<a NAME="E3:74_1_2"/>
<font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">s</font> where <font color="Olive" title="b1">s</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default">6 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 </span> } </span> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">t</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default">6 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> <span class="kw"> such that </span><br/><a NAME="E5:74_1_2"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 ;<br/>
<a NAME="E6:74_1_2"/>
<font color="Maroon" title="c3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">s</font> where <font color="Olive" title="b1">s</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default">6 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 </span> } </span> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">s</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default">6 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> <span class="kw"> such that </span><br/><a NAME="E8:74_1_2"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 ;<br/>
<a NAME="E9:74_1_2"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 8 &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 8 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:74_1_2"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="txt" href="#E8:74_1_2"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E10:74_1_2"/>
 for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> holds <br/><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="74_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">i</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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="c6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> implies <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:74_1_2_1"/>
<font color="Maroon" title="c6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</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="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/>

<a NAME="E2:74_1_2_1"/><span class="kw">then </span>
( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:74_1_2"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="ref" href="enumset1.html#D6" onmouseover="rs('enumset1/D6')" onmouseout="rh()">ENUMSET1:def 6</a>, <a class="ref" href="finseq_3.html#T6" onmouseover="rs('finseq_3/T6')" onmouseout="rh()">FINSEQ_3:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:74_1_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74_1_2"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E2:74_1_2"><span class="lab"><font color="Green" title="E35">A7</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E11:74_1_2"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:74_1_2"><span class="lab"><font color="Green" title="E38">A10</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/>


</div>
