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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: FINSEQ_5:27</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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">D</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="b4">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b3">D</font> holds <br/> ( (  for <font color="Olive" title="b5">f</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">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"><font color="Olive" title="b5">f</font> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> <font color="Olive" title="b2">n</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">f</font> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">i</font></span>)</span> ) &amp; ( <font color="Olive" title="b1">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"><font color="Olive" title="b4">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Olive" title="b2">n</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">i</font></span>)</span> ) )</div></div>
