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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: ZF_MODEL:1</font></span><br/></a><div class="add"> 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/> ( ( <font color="Olive" title="b1">H</font> is  <a href="zf_lang.html#V2" title="ZF_LANG:attr.2">being_equality</a>  implies  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K17" title="ZF_LANG:func.17">Var1</a> <font color="Olive" title="b1">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var2</a> <font color="Olive" title="b1">H</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="zf_lang.html#V3" title="ZF_LANG:attr.3">being_membership</a>  implies  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K17" title="ZF_LANG:func.17">Var1</a> <font color="Olive" title="b1">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var2</a> <font color="Olive" title="b1">H</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>  implies  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K19" title="ZF_LANG:func.19">the_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="zf_lang.html#V5" title="ZF_LANG:attr.5">conjunctive</a>  implies  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K20" title="ZF_LANG:func.20">the_left_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_right_argument_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive" title="b1">H</font> is  <a href="zf_lang.html#V6" title="ZF_LANG:attr.6">universal</a>  implies  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K23" title="ZF_LANG:func.23">the_scope_of</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K22" title="ZF_LANG:func.22">bound_in</a> <font color="Olive" title="b1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )</div></div>
