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<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>)</span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b1">n</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">n</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">  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>)</span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span><br/>



 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>) = 
 <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T40" target="_self" onmouseover="rs('newton05/T40')" onmouseout="rh()">PGC</a></span>
<br/>.= 
 <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton03.html#T4" onmouseover="rs('newton03/T4')" onmouseout="rh()">NEWTON03:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T46" target="_self" onmouseover="rs('newton05/T46')" onmouseout="rh()">PAN</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:74"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>)</span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T40" target="_self" onmouseover="rs('newton05/T40')" onmouseout="rh()">PGC</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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