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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: POLYNOM6:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b3">b1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Olive" title="b1">o1</font><br/>  for <font color="Olive" title="b4">b2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Olive" title="b2">o2</font><br/>  for <font color="Olive" title="b5">G</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">o1</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Olive" title="b2">o2</font></span>)</span></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Olive" title="b3">b1</font></span>)</span> &amp; (  for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Olive" title="b3">b1</font></span>)</span> holds <br/> ex <font color="Olive" title="b7">a19</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Olive" title="b1">o1</font> ex <font color="Olive" title="b8">Fk</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">o1</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Olive" title="b2">o2</font></span>)</span> st <br/>( <font color="Olive" title="b8">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">G</font> <a href="pre_poly.html#K9" title="PRE_POLY:func.9">/.</a> <font color="Olive" title="b6">i</font> &amp; <span class="p1">(<span class="default"><a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Olive" title="b3">b1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b6">i</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b7">a19</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b8">Fk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Olive" title="b4">b2</font></span>)</span> &amp; (  for <font color="Olive" title="b9">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b9">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b8">Fk</font> holds <br/> ex <font color="Olive" title="b10">a199</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Olive" title="b2">o2</font> st <br/>( <span class="p1">(<span class="default"><a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Olive" title="b4">b2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b9">m</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b10">a199</font> &amp; <font color="Olive" title="b8">Fk</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b9">m</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b7">a19</font> <a href="polynom6.html#K1" title="POLYNOM6:func.1">+^</a> <font color="Olive" title="b10">a199</font> ) ) ) ) holds <br/> <a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b1</font> <a href="polynom6.html#K1" title="POLYNOM6:func.1">+^</a> <font color="Olive" title="b4">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K5" title="PRE_POLY:func.5">FlattenSeq</a> <font color="Olive" title="b5">G</font></div></div>
