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<b>let </b><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c1">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">i2</font>
 ;<br/>

<a NAME="E2:41"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">i2</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E3:41"/>
<font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i1</font>
 
<b>by </b><i><a class="ref" href="binarith.html#T52" target="_self" title="BINARITH:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E4:41"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">i2</font>
 <b>by </b><i><a class="txt" href="binarith.html#E2:41"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>

<a NAME="E5:41"/><i><font color="Green" title="E30">A4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2
 
<b>by </b><i><a class="ref" href="binarith.html#T63" target="_self" title="BINARITH:th.63">Th63</a></i>;<br/>
<a NAME="E6:41"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#T52" target="_self" title="BINARITH:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E7:41"/>
<font color="Maroon" title="c1">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">i2</font>
 <b>by </b><i><a class="txt" href="binarith.html#E4:41"><i><font color="Green" title="E29">A3</font></i></a>, <a class="txt" href="binarith.html#E5:41"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>

<b>thus </b><a NAME="E8:41"/>
<font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">i2</font>
 <b>by </b><i><a class="txt" href="binarith.html#E1:41"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>


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