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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b3">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b2">k</font></span><br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font>; <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">k</font>, <font color="Olive" title="b2">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b2">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b2">m</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b1">k</font></span><br/><b>let </b><font color="Maroon" title="c3">k</font>, <font color="Maroon" title="c4">m</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c4">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c3">k</font></span><br/>







<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c4">m</font> = 
<font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">m</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_1.html#T49" target="_self" title="NAT_1:th.49">Th59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="ref" href="nat_1.html#T49" target="_self" title="NAT_1:th.49">Th59</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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