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<span class="kw">let </span><font color="Maroon" title="c6">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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">H</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> holds <br/> (  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">H</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H</font> &amp;  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Olive" title="b1">H</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</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="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">H</font> &amp;  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )</span><br/>



<a NAME="E1:12"/>
 <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>) is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a> 
 
;<br/>
<a NAME="E2:12"/><span class="kw">then </span>
 <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>)</span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T44" onmouseover="rs('zf_lang/T44')" onmouseout="rh()">ZF_LANG:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:12"/>
(  <a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">H</font> &amp;  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">H</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T3" onmouseover="rs('zf_lang/T3')" onmouseout="rh()">ZF_LANG:3</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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