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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: AOFA_L00:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <font color="Olive">b<sub>1</sub></font> <a href="aofa_l00.html#V6" title="AOFA_L00:attr.6">PC-correct</a>   <a href="aofa_l00.html#L1" title="AOFA_L00:struct.1">PCLangSignature</a> <br/>  for <font color="Olive" title="b3">L</font> being   <a href="aofa_l00.html#V17" title="AOFA_L00:attr.17">language</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">F</font> being   <a href="aofa_l00.html#NM5" title="AOFA_L00:NM.5">PC-theory</a> of <font color="Olive" title="b3">L</font><br/>  for <font color="Olive" title="b5">A</font>, <font color="Olive" title="b6">B</font>, <font color="Olive" title="b7">C</font> being   <a href="aofa_l00.html#NM3" title="AOFA_L00:NM.3">Formula</a> of <font color="Olive" title="b3">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b5">A</font> <a href="aofa_l00.html#K14" title="AOFA_L00:func.14">\or</a> <span class="p2">(<span class="default"><font color="Olive" title="b6">B</font> <a href="aofa_l00.html#K13" title="AOFA_L00:func.13">\and</a> <font color="Olive" title="b7">C</font></span>)</span></span>)</span> <a href="aofa_l00.html#K15" title="AOFA_L00:func.15">\imp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">A</font> <a href="aofa_l00.html#K14" title="AOFA_L00:func.14">\or</a> <font color="Olive" title="b6">B</font></span>)</span> <a href="aofa_l00.html#K13" title="AOFA_L00:func.13">\and</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">A</font> <a href="aofa_l00.html#K14" title="AOFA_L00:func.14">\or</a> <font color="Olive" title="b7">C</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">F</font></div></div>
