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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <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>   <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>   <a href="abcmiz_0.html#V1" title="ABCMIZ_0:attr.1">Noetherian</a>  non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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>  st <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> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Olive" title="b1">t</font> holds <br/><font color="Olive" title="b3">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">v1</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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>  st <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> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t</font> holds <br/><font color="Olive" title="b2">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">v1</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t</font> implies <font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t</font> )</span><br/>





<a NAME="E1:83"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">v2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:83"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<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> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font> <a href="abcmiz_0.html#R3" title="ABCMIZ_0:pred.3">is_applicable_to</a> <font color="Maroon" title="c2">t</font></span><br/>

<a NAME="E3:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <span class="p1">(<span class="default"><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> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T45" target="_self" title="ABCMIZ_0:th.45">Th45</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">i</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="abcmiz_0.html#D21" target="_self" title="ABCMIZ_0:def.21">ABCMIZ_0:def 21</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">s</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font>  st <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> &amp; <font color="Olive" title="b2">s</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<font color="Maroon" title="c2">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> holds <br/><font color="Olive" title="b1">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Olive" title="b2">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font>  st <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> &amp; <font color="Olive" title="b1">s</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<font color="Maroon" title="c2">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> holds <br/><font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Olive" title="b1">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">s</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> &amp; <font color="Maroon" title="c7">s</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<font color="Maroon" title="c2">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> implies <font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c7">s</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E4:83"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:83"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
 <span class="kw">and </span><br/><a NAME="E6:83"/><span class="lab"><font color="Green" title="E53">A6</font></span>: 
<font color="Maroon" title="c7">s</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<font color="Maroon" title="c2">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c7">s</font></span><br/>

<a NAME="E7:83"/><span class="lab"><font color="Green" title="E54">A7</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:83"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E8:83"/><span class="lab"><font color="Green" title="E55">A8</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#D19" target="_self" title="ABCMIZ_0:def.19">Def19</a></span>;<br/>
<a NAME="E9:83"/><span class="lab"><font color="Green" title="E56">A9</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">v1</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">v2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E10:83"/>
<font color="Maroon" title="c5">i</font> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<a NAME="E11:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A10</font></span>: 
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E12:83"/>
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<a NAME="E13:83"/><span class="kw">then </span>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <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="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<font color="Maroon" title="c2">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:83"><span class="lab"><font color="Green" title="E57">A10</font></span></a>, <a class="txt" href="#E8:83"><span class="lab"><font color="Green" title="E55">A8</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<a NAME="E14:83"/><span class="kw">then </span>
<font color="Maroon" title="c7">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <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="c4">v2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">v1</font></span>)</span>,<font color="Maroon" title="c2">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:83"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E15:83"/><span class="kw">then </span>
<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> <a href="abcmiz_0.html#K8" title="ABCMIZ_0:func.8">ast</a> <font color="Maroon" title="c2">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E9:83"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="abcmiz_0.html#T47" target="_self" title="ABCMIZ_0:th.47">Th47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:83"/>
<font color="Maroon" title="c6">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E9:83"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E7:83"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="abcmiz_0.html#T24" target="_self" title="ABCMIZ_0:th.24">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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