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<div>:: <span class="kw">deftheorem </span>   defines <a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <a onclick="hs(this)" href="javascript:()">SUBSTUT1:def 36 : <br/></a><span> for <font color="Olive" title="b1">A</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">Z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="substut1.html#K1" title="SUBSTUT1:func.1">vSUB</a> <font color="Olive" title="b1">A</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> ( (  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K34" title="SUBSTUT1:func.34">`2</a></span>)</span>)</span>)</span> implies  <a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <span class="p1">(<span class="default"><a href="substut1.html#K13" title="SUBSTUT1:func.13">upVar</a> (<span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<span class="p3">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K34" title="SUBSTUT1:func.34">`2</a></span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K22" title="QC_LANG1:func.22">the_scope_of</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span></span>)</span>)</span>)</span> ) &amp; (  not  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K34" title="SUBSTUT1:func.34">`2</a></span>)</span>)</span>)</span> implies  <a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a></span>)</span> ) );<br/></span></div>
