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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">T</font>  ex <font color="Olive" title="b2">NS</font> being <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> st <font color="Olive" title="b1">S</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">NS</font></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">NS</font> being <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> st <font color="Maroon" title="c2">S</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">NS</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c3">NS</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  as  <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="frechet2.html#E7"><i><font color="Green" title="E7">Lm6</font></i></a>, <a class="txt" href="frechet2.html#E8"><i><font color="Green" title="E8">Lm7</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">NS</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">S</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">NS</font></span><br/>

<b>thus </b><a NAME="E2:9"/>
<font color="Maroon" title="c2">S</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">S</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">NS</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</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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