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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E57">Th56</font></span>: <a NAME="T61"><span class="comment"><font color="firebrick">:: AOFA_A00:61</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">N</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">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>  1,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="aofa_a00.html#V21" title="AOFA_A00:attr.21">-array</a>   <a href="aofa_a00.html#L5" title="AOFA_A00:struct.5">ConnectivesSignature</a> <br/>  for <font color="Olive" title="b4">Y</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b4">Y</font>  st (  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="aofa_a00.html#U7" title="AOFA_A00:sel.7">connectives</a> of <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <font color="Olive" title="b4">Y</font> or <font color="Olive" title="b5">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"> the <a href="aofa_a00.html#U7" title="AOFA_A00:sel.7">connectives</a> of <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a>  ) &amp; <font color="Olive" title="b5">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <font color="Olive" title="b1">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">Y</font> holds <br/> ex <font color="Olive" title="b6">A</font> being   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b3">S</font> st <br/>( <font color="Olive" title="b6">A</font> is 1,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">N</font> <a href="aofa_a00.html#V22" title="AOFA_A00:attr.22">-array</a>  &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b6">A</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b5">X</font> )</div></div>
