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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th52</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: ORDEQ_01:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">y0</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b5">G</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b2">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b5">G</font> <a href="nfcont_1.html#R5" title="NFCONT_1:pred.5">is_Lipschitzian_on</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span> holds <br/> ex <font color="Olive" title="b6">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st  <a href="abian.html#K1" title="ABIAN:func.1">iter</a> (<span class="p1">(<span class="default"><a href="ordeq_01.html#K6" title="ORDEQ_01:func.6">Fredholm</a> (<font color="Olive" title="b5">G</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">y0</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b6">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>) is  <a href="nfcont_2.html#V1" title="NFCONT_2:attr.1">contraction</a> </div></div>
