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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">p</font>, <font color="Olive" title="b2">q</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Olive" title="b3">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Olive" title="b2">q</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</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">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Olive" title="b1">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> (  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c4">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> implies  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:135"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c4">n</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</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">  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E2:135"/>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c4">n</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T81" target="_self" onmouseover="rs('afinsq_1/T81')" onmouseout="rh()">Th78</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:135"/>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:135"><span class="lab"><font color="Green" title="E52">A1</font></span></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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