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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">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">  for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <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> holds   <a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>)</span>)</span>,<font color="Olive" title="b2">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</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_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <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>; <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">  <a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span>,<font color="Maroon" title="c3">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font></span><br/>



<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="32_1"><span class="kw">now </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">  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p2">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Olive" title="b1">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Olive" title="b1">j</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">j</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="c4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> implies <span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p2">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font> )</span><br/><span class="kw">assume </span><a NAME="E1:32_1"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</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"> <span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p2">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p2">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="descip_1.html#D4" target="_self" onmouseover="rs('descip_1/D4')" onmouseout="rh()">Def4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="descip_1.html#D4" target="_self" onmouseover="rs('descip_1/D4')" onmouseout="rh()">Def4</a></span>
<br/>.= 
<font color="Maroon" title="c2">s</font> <a href="descip_1.html#K10" title="DESCIP_1:func.10">.</a> <font color="Maroon" title="c4">j</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T72" onmouseover="rs('xboolean/T72')" onmouseout="rh()">XBOOLEAN:72</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="E2:32"/>
 <a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<span class="p1">(<span class="default"><a href="descip_1.html#K11" title="DESCIP_1:func.11">Op-XOR</a> (<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>)</span>)</span>,<font color="Maroon" title="c3">t</font>) <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="ref" href="finseq_2.html#T119" onmouseover="rs('finseq_2/T119')" onmouseout="rh()">FINSEQ_2:119</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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