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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="stacks_1.html#NM3" title="STACKS_1:NM.3">StackAlgebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Maroon" title="c1">X</font>  st  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Olive" title="b1">s</font> holds <br/> <a href="stacks_1.html#K13" title="STACKS_1:func.13">core</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="stacks_1.html#NM2" title="STACKS_1:NM.2">stack</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c2">s</font> implies  <a href="stacks_1.html#K13" title="STACKS_1:func.13">core</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">R</font> =  <a href="stacks_1.html#K12" title="STACKS_1:func.12">ConstructionRed</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">assume </span><a NAME="E1:63"/><span class="lab"><font color="Green" title="E40">A0</font></span>: 
 <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c2">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="stacks_1.html#K13" title="STACKS_1:func.13">core</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">t</font> being   the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="stacks_1.html#K12" title="STACKS_1:func.12">ConstructionRed</a> <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:63"/><span class="lab"><font color="Green" title="E41">A1</font></span>: 
( <font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> &amp; <font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stacks_1.html#K13" title="STACKS_1:func.13">core</a> <font color="Maroon" title="c2">s</font> )
 <span class="kw">and </span><br/><a NAME="E4:63"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">t</font> holds <br/>(  not  <a href="stacks_1.html#R1" title="STACKS_1:pred.1">emp</a> <font color="Maroon" title="c4">t</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font> &amp; <font color="Maroon" title="c4">t</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stacks_1.html#K5" title="STACKS_1:func.5">pop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="stacks_1.html#D19" target="_self" title="STACKS_1:def.19">CORE</a></span>;<br/>
<a NAME="E5:63"/><span class="lab"><font color="Green" title="E43">A3</font></span>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></span>;<br/>
<a NAME="E6:63"/><span class="kw">then </span>
<font color="Maroon" title="c4">t</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E7:63"/><span class="kw">then </span>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">t</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E40">A0</font></span></a>, <a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E43">A3</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:63"/>
 <a href="stacks_1.html#K13" title="STACKS_1:func.13">core</a> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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