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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th25</font></span>: <a NAME="T26"><span class="comment"><font color="firebrick">:: AOFA_L00:26</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">number</a> <br/>  for <font color="Olive" title="b2">X</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="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>  <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#V7" title="AOFA_L00:attr.7">QC-correct</a>   <a href="aofa_l00.html#L2" title="AOFA_L00:struct.2">QCLangSignature</a> over <font color="Olive" title="b2">X</font><br/>  for <font color="Olive" title="b4">Q</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="b3">S</font> holds <br/> (  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</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> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 5</span>)</span></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b3">S</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>) &amp; (  for <font color="Olive" title="b5">A</font> being   <a href="aofa_l00.html#NM3" title="AOFA_L00:NM.3">Formula</a> of <font color="Olive" title="b4">Q</font> holds <br/> ( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b5">A</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</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> <font color="Olive" title="b1">n</font></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b3">S</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>) &amp; (  for <font color="Olive" title="b6">B</font> being   <a href="aofa_l00.html#NM3" title="AOFA_L00:NM.3">Formula</a> of <font color="Olive" title="b4">Q</font> holds <br/> ( <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b5">A</font>,<font color="Olive" title="b6">B</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</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> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b3">S</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>) &amp;  ...  &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b5">A</font>,<font color="Olive" title="b6">B</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</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> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 4</span>)</span></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b3">S</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>) &amp; (  for <font color="Olive" title="b7">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">X</font> holds <br/> ( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b5">A</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"> the <a href="aofa_l00.html#U3" title="AOFA_L00:sel.3">quantifiers</a> of <font color="Olive" title="b3">S</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive" title="b7">x</font>)</span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b3">S</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>) &amp; <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b5">A</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"> the <a href="aofa_l00.html#U3" title="AOFA_L00:sel.3">quantifiers</a> of <font color="Olive" title="b3">S</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (2,<font color="Olive" title="b7">x</font>)</span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b3">S</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>) ) ) ) ) ) ) )</div></div>
