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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" title="c4">m</font>, <font color="Maroon" title="c5">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:30_1_1_1"/>
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">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>
 ;<br/><a NAME="E2:30_1_1_1"/><b>then </b><i><font color="Green" title="E21">A1</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">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="E3:30_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="E4:30_1_1_1"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">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#K1" title="RELAT_1:func.1">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="E5:30_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>
 ;<br/><a NAME="E6:30_1_1_1"/><b>then </b>
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">I</font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E2:30_1_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="scmpds_3.html#D5" title="SCMPDS_3:def.5">SCMPDS_3:def 5</a></i>;<br/><b>hence </b><a NAME="E7:30_1_1_1"/>
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">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#E4:30_1_1_1"><i><font color="Green" title="E22">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:30_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="scmpds_3.html#V1" title="SCMPDS_3:attr.1">initial</a>
 <b>by </b><i><a class="ref" href="scmpds_3.html#D5" title="SCMPDS_3:def.5">SCMPDS_3:def 5</a></i>;<br/>


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