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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:30_1_1_1"/>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">I</font></span>)</span>
 ;<br/><a NAME="E2:30_1_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/><a NAME="E3:30_1_1_1"/>
<font color="Maroon">I</font> <a href="tarski.html#R1">c=</a>  <a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T9">SCMPDS_4:9</a></i>;<br/><a NAME="E4:30_1_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>assume </b><a NAME="E5:30_1_1_1"/>
<font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E6:30_1_1_1"/><b>then </b>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="scmpds_3.html#D5">SCMPDS_3:def 5</a></i>;<br/><b>hence </b><a NAME="E7:30_1_1_1"/>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:30_1_1"/>
 <a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">I</font> is <a href="scmpds_3.html#V1">initial</a>
 <b>by </b><i><a class="ref" href="scmpds_3.html#D5">SCMPDS_3:def 5</a></i>;<br/>


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