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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">m</font>, <font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span> &amp; <font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span> )</span><br/><b>assume </b><a NAME="E1:26_1_1_1"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span> )</span><br/><a NAME="E2:26_1_1_1"/><b>then </b><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T8" target="_self" title="SCMPDS_7:th.8">Th8</a></i>;<br/><a NAME="E3:26_1_1_1"/>
<font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T9" title="SCMPDS_4:th.9">SCMPDS_4:9</a></i>;<br/><a NAME="E4:26_1_1_1"/><b>then </b><i><font color="Green" title="E21">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/><b>assume </b><a NAME="E5:26_1_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span></span><br/><a NAME="E6:26_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E2:26_1_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="scmnorm.html#D1" title="SCMNORM:def.1">SCMNORM:def 1</a></i>;<br/><b>hence </b><a NAME="E7:26_1_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E4:26_1_1_1"><i><font color="Green" title="E21">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/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:26_1_1"/>
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <font color="Maroon" title="c3">I</font> is <a href="scmnorm.html#V1" title="SCMNORM:attr.1">initial</a>
 <b>by </b><i><a class="ref" href="scmnorm.html#D1" title="SCMNORM:def.1">SCMNORM:def 1</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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