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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E63">Th62</font></span>: <a NAME="T67"><span class="comment"><font color="firebrick">:: AOFA_A00:67</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">s</font>, <font color="Olive" title="b4">r</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">S1</font>, <font color="Olive" title="b6">S2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="aofa_a00.html#L5" title="AOFA_A00:struct.5">ConnectivesSignature</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a>  the <a href="aofa_a00.html#U7" title="AOFA_A00:sel.7">connectives</a> of <font color="Olive" title="b5">S1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 3 &amp; (  for <font color="Olive" title="b7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b7">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b7">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 3 holds <br/>(  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Olive" title="b5">S1</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="b5">S1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Olive" title="b6">S2</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="b6">S2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b7">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> &amp;  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b5">S1</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="b5">S1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b6">S2</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="b6">S2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b7">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> ) ) &amp; <font color="Olive" title="b6">S2</font> is <font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b4">r</font> <a href="aofa_a00.html#V21" title="AOFA_A00:attr.21">-array</a>  holds <br/><font color="Olive" title="b5">S1</font> is <font color="Olive" title="b1">n</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b4">r</font> <a href="aofa_a00.html#V21" title="AOFA_A00:attr.21">-array</a> </div></div>
