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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: FOMODEL0:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">q1</font>, <font color="Olive" title="b5">q2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b2">p1</font> is <font color="Olive" title="b1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Olive" title="b4">q1</font> is <font color="Olive" title="b1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; ( <font color="Olive" title="b2">p1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b5">q2</font> or <font color="Olive" title="b3">p2</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q2</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">q1</font> ) holds <br/>( <font color="Olive" title="b2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q1</font> &amp; <font color="Olive" title="b3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q2</font> )</div></div>
