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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</font> holds  <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">v2</font></span>)</span>,<font color="Olive" title="b1">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">v1</font></span>)</span> <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> <font color="Olive" title="b2">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Olive" title="b1">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">t</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</font> holds  <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">v2</font></span>)</span>,<font color="Maroon" title="c2">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">v1</font></span>)</span> <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> <font color="Olive" title="b1">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">v2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">v2</font></span>)</span>,<font color="Maroon" title="c2">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">v1</font></span>)</span> <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> <font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font></span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">v</font> = <font color="Maroon" title="c3">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">v2</font>;<br/>
<a NAME="E1:69"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<font color="Maroon" title="c4">v2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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">v2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D19" target="_self" onmouseover="rs('abcmiz_0/D19')" onmouseout="rh()">Def19</a></span>;<br/>
<a NAME="E2:69"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
 <a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">v2</font></span>)</span>,<font color="Maroon" title="c2">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">t</font>)</span>)</span> <a href="rewrite1.html#K1" title="REWRITE1:func.1">$^</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<font color="Maroon" title="c4">v2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T34" target="_self" onmouseover="rs('abcmiz_0/T34')" onmouseout="rh()">Th34</a></span>;<br/>
<a NAME="E3:69"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c2">t</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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="c3">v1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D19" target="_self" onmouseover="rs('abcmiz_0/D19')" onmouseout="rh()">Def19</a></span>;<br/>
<a NAME="E4:69"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">v2</font></span>)</span>,<font color="Maroon" title="c2">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<font color="Maroon" title="c4">v2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="abcmiz_0.html#T33" target="_self" onmouseover="rs('abcmiz_0/T33')" onmouseout="rh()">Th33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:69"/>
<span class="p1">(<span class="default"><a href="abcmiz_0.html#K7" title="ABCMIZ_0:func.7">apply</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">v2</font></span>)</span>,<font color="Maroon" title="c2">t</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">v1</font></span>)</span> <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> <font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D19" target="_self" onmouseover="rs('abcmiz_0/D19')" onmouseout="rh()">Def19</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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