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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</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> holds   <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <span class="p1">(<span class="default"><a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<font color="Olive" title="b1">n</font>)</span>)</span></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">  <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <span class="p1">(<span class="default"><a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">n</font>)</span>)</span></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">p</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Maroon" title="c1">R</font></span>)</span>,<span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Maroon" title="c1">R</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:101"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
( <font color="Maroon" title="c3">p</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) &amp; <font color="Maroon" title="c3">p</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Maroon" title="c1">R</font></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E3:101"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c3">p</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#D11" target="_self" onmouseover="rs('funct_7/D11')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E4:101"/>
<font color="Maroon" title="c3">p</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101"><span class="lab"><font color="Green" title="E51">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:101"/>
 <a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <span class="p1">(<span class="default"><a href="funct_7.html#K8" title="FUNCT_7:func.8">iter</a> (<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E3:101"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="funct_7.html#D11" target="_self" onmouseover="rs('funct_7/D11')" onmouseout="rh()">Def10</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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