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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a>   <a href="compos_1.html#V6" title="COMPOS_1:attr.6">homogeneous</a>   <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a>   <a href="compos_1.html#L1" title="COMPOS_1:struct.1">COM-Struct</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">I</font> being   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</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="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Olive" title="b1">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <font color="Maroon" title="c1">S</font>; <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">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</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="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> implies <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:105"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<font color="Maroon" title="c3">x</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="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span>
 ; <a class="txt" 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="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span><br/>

<a NAME="E2:105"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p1">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span>
 
;<br/>
<span class="lab"><font color="Green" title="E45">A3</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> = 
 <a href="card_3.html#K9" title="CARD_3:func.9">DOM</a> <span class="p1">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p2">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#T75" title="CARD_3:th.75">CARD_3:75</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:105"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="card_3.html#D11" title="CARD_3:def.11">CARD_3:def 11</a></span>
;<br/>
<a NAME="E4:105"/>
<span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> (<span class="p1">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p2">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">x</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:105"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:105"/>
<span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:105"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E3:105"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="card_3.html#T76" title="CARD_3:th.76">CARD_3:76</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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