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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> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font> holds <br/>( <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="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> <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> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font> implies ( <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="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> <font color="Maroon" title="c3">t</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:97"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</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="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="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> <font color="Maroon" title="c3">t</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">u</font> = <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>;<br/>
<a NAME="E2:97"/>
<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="#E1:97"><span class="lab"><font color="Green" title="E61">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:97"/>
<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="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="polnot_1.html#D22" target="_self" onmouseover="rs('polnot_1/D22')" onmouseout="rh()">Def22</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> <font color="Maroon" title="c3">t</font></span><br/>

<span class="kw">hence </span><a NAME="E4:97"/>
<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> <font color="Maroon" title="c3">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polnot_1.html#D23" target="_self" onmouseover="rs('polnot_1/D23')" onmouseout="rh()">Def23</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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