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<a NAME="E1:73_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/>
<a NAME="E2:73_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_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="E1:73_1_1_1"/>
( <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73_1_1"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:73_1_1_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:73_1_1_1_1"/>
(  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_3.html#T10" onmouseover="rs('int_3/T10')" onmouseout="rh()">INT_3:10</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="73_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:73_1_1_1_2"/>
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ; <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="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:73_1_1_1_2"/>
(  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c2">n</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_3.html#T11" onmouseover="rs('int_3/T11')" onmouseout="rh()">INT_3:11</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>

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