<?xml version="1.0"?>
<div><div><a NAME="S1"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: YELLOW15:sch 1</font></span><br/></a><span class="lab"><font color="Green" title="E1">SeqLambda1C</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  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> , <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ], <font color="Maroon">F<sub>3</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>4</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  } :<br/><div class="add"><a NAME="E2:1"/>
 ex <font color="Olive" title="b1">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon">F<sub>2</sub></font>() st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; (  for <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">i</font>] implies <font color="Olive" title="b1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b2">i</font>) ) &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">i</font>] implies <font color="Olive" title="b1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b2">i</font>) ) ) ) )
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">i</font>] implies <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">i</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() ) &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">i</font>] implies <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b1">i</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() ) )
 </div></div></div>
