<?xml version="1.0"?>
<div class="add">

<div><span class="kw">hereby </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  ) implies <font color="Maroon" title="c1">S</font> is  <a href="glpacy00.html#V5" title="GLPACY00:attr.5">Cycle-like</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:75_1_1_1"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<font color="Maroon" title="c1">S</font> is  <a href="glpacy00.html#V5" title="GLPACY00:attr.5">Cycle-like</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> </span><br/><a NAME="E2:75_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glpacy00.html#E18"><span class="lab"><font color="Green" title="E18">Lm2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:75_1_1_1"/>
<font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75_1_1_1"><span class="lab"><font color="Green" title="E43">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:75_1_1"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">S</font> is  <a href="glpacy00.html#V5" title="GLPACY00:attr.5">Cycle-like</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c1">S</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glpacy00.html#D8" target="_self" onmouseover="rs('glpacy00/D8')" onmouseout="rh()">GLPACY00:def 8</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> </span><br/>

<span class="kw">thus </span><a NAME="E3:75_1_1"/>
<font color="Maroon" title="c1">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1_1"><span class="lab"><font color="Green" title="E43">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
