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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="polnot_1.html#NM3" title="POLNOT_1:NM.3">Polish-language</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">  for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">s</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  holds <br/>( <font color="Olive" title="b1">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">t</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">t</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">t</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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="c2">s</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  implies ( <font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:103"/>
<font color="Maroon" title="c2">s</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</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="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a>  &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">q</font>, <font color="Maroon" title="c5">r</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E3:103"/><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">and </span><br/><a NAME="E4:103"/><span class="lab"><font color="Green" title="E66">A2</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">r</font>
 ;<br/>
<a NAME="E5:103"/><span class="lab"><font color="Green" title="E67">A3</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:103"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="finseq_1.html#T32" onmouseover="rs('finseq_1/T32')" onmouseout="rh()">FINSEQ_1:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:103"/>
<font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> is <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#V5" title="POLNOT_1:attr.5">-headed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E65">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="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> = 
<font color="Maroon" title="c4">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="txt" href="#E5:103"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="polnot_1.html#T52" target="_self" onmouseover="rs('polnot_1/T52')" onmouseout="rh()">Th52</a></span>
<br/>.= 
<font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K15" title="POLNOT_1:func.15">-head</a> <font color="Maroon" title="c2">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="txt" href="#E4:103"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="polnot_1.html#T52" target="_self" onmouseover="rs('polnot_1/T52')" onmouseout="rh()">Th52</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="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font></span>)</span> = 
<font color="Maroon" title="c5">r</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="txt" href="#E5:103"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="polnot_1.html#T52" target="_self" onmouseover="rs('polnot_1/T52')" onmouseout="rh()">Th52</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="polnot_1.html#K16" title="POLNOT_1:func.16">-tail</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="txt" href="#E4:103"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="polnot_1.html#T52" target="_self" onmouseover="rs('polnot_1/T52')" onmouseout="rh()">Th52</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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