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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">h</font> be   <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"> ( <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> implies  for <font color="Olive" title="b1">S</font> being    <a href="number14.html#M1" title="NUMBER14:mode.1">Sierp45FS</a> of <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>  st <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a>  holds <br/> for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">n</font>, <a href="number14.html#K3" title="NUMBER14:func.3">numberR</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 2 &amp; <font color="Olive" title="b2">n</font>, <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 3 &amp; (  for <font color="Olive" title="b3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">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="Olive" title="b1">S</font> holds <br/><font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> ) holds <br/><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:55"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
<font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></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">  for <font color="Olive" title="b1">S</font> being    <a href="number14.html#M1" title="NUMBER14:mode.1">Sierp45FS</a> of <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>  st <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a>  holds <br/> for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">n</font>, <a href="number14.html#K3" title="NUMBER14:func.3">numberR</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 2 &amp; <font color="Olive" title="b2">n</font>, <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 3 &amp; (  for <font color="Olive" title="b3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">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="Olive" title="b1">S</font> holds <br/><font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> ) holds <br/><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">S</font> be    <a href="number14.html#M1" title="NUMBER14:mode.1">Sierp45FS</a> of <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</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">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a>  implies  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">n</font>, <a href="number14.html#K3" title="NUMBER14:func.3">numberR</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 2 &amp; <font color="Olive" title="b1">n</font>, <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 3 &amp; (  for <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">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="c5">S</font> holds <br/><font color="Olive" title="b1">n</font>,<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> ) holds <br/><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:55"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</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>  st <font color="Olive" title="b1">n</font>, <a href="number14.html#K3" title="NUMBER14:func.3">numberR</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 2 &amp; <font color="Olive" title="b1">n</font>, <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 3 &amp; (  for <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">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="c5">S</font> holds <br/><font color="Olive" title="b1">n</font>,<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> ) holds <br/><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">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"> ( <font color="Maroon" title="c6">n</font>, <a href="number14.html#K3" title="NUMBER14:func.3">numberR</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 2 &amp; <font color="Maroon" title="c6">n</font>, <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 3 &amp; (  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="c5">S</font> holds <br/><font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) implies <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:55"/><span class="lab"><font color="Green" title="E47">A3</font></span>: 
<font color="Maroon" title="c6">n</font>, <a href="number14.html#K3" title="NUMBER14:func.3">numberR</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 2
 <span class="kw">and </span><br/><a NAME="E4:55"/><span class="lab"><font color="Green" title="E48">A4</font></span>: 
<font color="Maroon" title="c6">n</font>, <a href="number14.html#K4" title="NUMBER14:func.4">numberR0</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 3
 <span class="kw">and </span><br/><a NAME="E5:55"/><span class="lab"><font color="Green" title="E49">A5</font></span>: 
 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="c5">S</font> holds <br/><font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</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">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</a> </span><br/>

<span class="kw">assume </span><a NAME="E6:55"/>
 not <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="number03.html#R1" title="NUMBER03:pred.1">are_mutually_coprime</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"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:55_1"/><span class="kw">then </span>
(  not <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  or  not <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  or  not <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1"><span class="kw">suppose </span></a><a NAME="E1:55_1_1"/>
 not <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</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"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:55_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="txt" href="number14.html#E61"><span class="lab"><font color="Green" title="E41">Lm7</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_2"><span class="kw">suppose </span></a><a NAME="E1:55_1_2"/>
 not <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</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"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:55_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="txt" href="number14.html#E62"><span class="lab"><font color="Green" title="E42">Lm8</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_3"><span class="kw">suppose </span></a><a NAME="E1:55_1_3"/>
 not <font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</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"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:55_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="txt" href="number14.html#E63"><span class="lab"><font color="Green" title="E43">Lm9</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></div><span class="kw">end;</span></div>

</div>
