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<div>:: <span class="kw">deftheorem </span>   defines <a href="measur13.html#K13" title="MEASUR13:func.13">ProjPMap1</a> <a onclick="hs(this)" href="javascript:()">MEASUR13:def 16 : <br/></a><span> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="measur13.html#K3" title="MEASUR13:func.3">CarProduct</a> <font color="Olive" title="b2">X</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="measur13.html#K3" title="MEASUR13:func.3">CarProduct</a> <span class="p1">(<span class="default"><a href="measur13.html#K4" title="MEASUR13:func.4">SubFin</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b1">n</font>)</span>)</span><br/>  for <font color="Olive">b<sub>5</sub></font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="measur13.html#K1" title="MEASUR13:func.1">ElmFin</a> (<font color="Olive" title="b2">X</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measur13.html#K13" title="MEASUR13:func.13">ProjPMap1</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">x</font>) iff  ex <font color="Olive" title="b6">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="measur13.html#K3" title="MEASUR13:func.3">CarProduct</a> <span class="p3">(<span class="default"><a href="measur13.html#K4" title="MEASUR13:func.4">SubFin</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="measur13.html#K1" title="MEASUR13:func.1">ElmFin</a> (<font color="Olive" title="b2">X</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> st <br/>( <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g</font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="mesfun12.html#K2" title="MESFUN12:func.2">ProjPMap1</a> (<font color="Olive" title="b6">g</font>,<font color="Olive" title="b4">x</font>) ) );<br/></span></div>
