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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> holds   <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</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">  for <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> holds   <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>; <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">  <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font></span><br/>





<a NAME="E1:116"/><span class="lab"><font color="Green" title="E58">A1</font></span>: 
( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
;<br/>
<a NAME="E2:116"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E3:116"/><span class="lab"><font color="Green" title="E60">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 
;<br/>
<a NAME="E4:116"/><span class="kw">then </span>
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:116"><span class="lab"><font color="Green" title="E59">A2</font></span></a>, <a class="ref" href="funct_7.html#T74" target="_self" onmouseover="rs('funct_7/T74')" onmouseout="rh()">Th73</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">R</font> =  <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">n</font>) as   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a></span>;<br/>
<a NAME="E6:116"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:116"><span class="lab"><font color="Green" title="E59">A2</font></span></a>, <a class="txt" href="#E3:116"><span class="lab"><font color="Green" title="E60">A3</font></span></a>, <a class="ref" href="funct_7.html#T74" target="_self" onmouseover="rs('funct_7/T74')" onmouseout="rh()">Th73</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:116"/>
 <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">n</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:116"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</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/>


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