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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ] <b>means </b><font color="Maroon" title="c1">a</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c1">a</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>;<br/>
<a NAME="E1:88_1_1"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ]
 
<b>by </b><i><a class="ref" href="ordinal2.html#T44" target="_self" title="ORDINAL2:th.44">Th44</a></i>;<br/>
<div><i><font color="Green" title="E37">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="88_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">b</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">b</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c3">b</font>] )</span><br/><b>assume </b><a NAME="E1:88_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">b</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c3">b</font>]</span><br/><b>then reconsider </b><font color="Maroon" title="c4">c</font> = <font color="Maroon" title="c1">a</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c3">b</font> as  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  ;<br/><a NAME="E3:88_1_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="ordinal2.html#T45" target="_self" title="ORDINAL2:th.45">Th45</a></i>;<br/><b>hence </b><a NAME="E4:88_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c3">b</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>thus </b><a NAME="E3:88_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">b</font>]
 <b>from </b><i><a class="ref" href="ordinal2.html#S17" target="_self" title="ORDINAL2:sch.17">ORDINAL2:sch 17</a>(<a class="txt" href="ordinal2.html#E1:88_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="ordinal2.html#E2:88_1_1"><i><font color="Green" title="E37">A2</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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