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<a NAME="E1:43_1_1"/><i><font color="Green" title="E37">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">Nseq1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="seqm_3.html#D8" target="_self" title="SEQM_3:def.8">Def8</a></i>;<br/>
<a NAME="E2:43_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K3" title="SEQM_3:func.3">*</a> <font color="Maroon" title="c1">Nseq</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">Nseq1</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></i>;<br/>
<a NAME="E3:43_1_1"/><b>then </b><i><font color="Green" title="E38">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K3" title="SEQM_3:func.3">*</a> <font color="Maroon" title="c1">Nseq</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="txt" href="seqm_3.html#E1:43_1_1"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">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/><a NAME="E1:43_1_1_1"/>
<font color="Maroon" title="c1">Nseq</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">Nseq</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="seqm_3.html#E10"><i><font color="Green" title="E10">Lm6</font></i></a></i>;<br/><a NAME="E2:43_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">Nseq</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">Nseq</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seqm_3.html#T7" target="_self" title="SEQM_3:th.7">Th7</a></i>;<br/><a NAME="E3:43_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K3" title="SEQM_3:func.3">*</a> <font color="Maroon" title="c1">Nseq</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">Nseq</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seqm_3.html#T31" target="_self" title="SEQM_3:th.31">Th31</a></i>;<br/><b>hence </b><a NAME="E4:43_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K3" title="SEQM_3:func.3">*</a> <font color="Maroon" title="c1">Nseq</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">Nseq1</font> <a href="seqm_3.html#K3" title="SEQM_3:func.3">*</a> <font color="Maroon" title="c1">Nseq</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="seqm_3.html#T31" target="_self" title="SEQM_3:th.31">Th31</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:43_1_1"/>
<font color="Maroon" title="c1">Nseq</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">Nseq1</font> is  <a href="seqm_3.html#V1" title="SEQM_3:attr.1">increasing</a> <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E3:43_1_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="seqm_3.html#D8" target="_self" title="SEQM_3:def.8">Def8</a>, <a class="txt" href="seqm_3.html#E10"><i><font color="Green" title="E10">Lm6</font></i></a></i>;<br/>


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