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<span class="kw">let </span><font color="Maroon" title="c1">fp</font> be    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c1">fp</font> holds <br/><font color="Maroon" title="c1">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Product</a> <font color="Maroon" title="c1">fp</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c1">fp</font> implies <font color="Maroon" title="c1">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Product</a> <font color="Maroon" title="c1">fp</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:45"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c1">fp</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Product</a> <font color="Maroon" title="c1">fp</font></span><br/>

<a NAME="E2:45"/><span class="kw">then </span>
<font color="Maroon" title="c1">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c1">fp</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T3" title="FUNCT_1:th.3">FUNCT_1:3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:45"/>
<font color="Maroon" title="c1">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Product</a> <font color="Maroon" title="c1">fp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#T7" title="NAT_3:th.7">NAT_3:7</a></span>; <a class="txt" 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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