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<span class="kw">let </span><font color="Maroon" title="c1">B</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">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><br/>  for <font color="Olive" title="b2">S1</font>, <font color="Olive" title="b3">S2</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>  st <font color="Olive" title="b2">S1</font> is <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  &amp; <font color="Olive" title="b3">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  holds <br/><font color="Olive" title="b2">S1</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Olive" title="b3">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</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">S1</font>, <font color="Olive" title="b2">S2</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>  st <font color="Olive" title="b1">S1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  &amp; <font color="Olive" title="b2">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  holds <br/><font color="Olive" title="b1">S1</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Olive" title="b2">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">S1</font>, <font color="Maroon" title="c4">S2</font> be   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</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"> ( <font color="Maroon" title="c3">S1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  &amp; <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  implies <font color="Maroon" title="c3">S1</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:25"/>
( <font color="Maroon" title="c3">S1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  &amp; <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</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"> <font color="Maroon" title="c3">S1</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">P1</font>, <font color="Maroon" title="c6">P2</font> being   <a href="proofs_1.html#NM4" title="PROOFS_1:NM.4">Formula-sequence</a><span class="kw"> such that </span><br/><a NAME="E3:25"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c5">P1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V2" title="PROOFS_1:attr.2">-correct</a> 
 <span class="kw">and </span><br/><a NAME="E4:25"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
<font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="proofs_1.html#K1" title="PROOFS_1:func.1">rng</a> <font color="Maroon" title="c5">P1</font>
 <span class="kw">and </span><br/><a NAME="E5:25"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
<font color="Maroon" title="c6">P2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V2" title="PROOFS_1:attr.2">-correct</a> 
 <span class="kw">and </span><br/><a NAME="E6:25"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
<font color="Maroon" title="c4">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="proofs_1.html#K1" title="PROOFS_1:func.1">rng</a> <font color="Maroon" title="c6">P2</font>
 ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">P</font> = <font color="Maroon" title="c5">P1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c6">P2</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">S</font> =  <a href="proofs_1.html#K1" title="PROOFS_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c6">P2</font></span>)</span> as   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a> ;<br/>
<a NAME="E8:25"/>
<font color="Maroon" title="c8">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S1</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Maroon" title="c4">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E6:25"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="finseq_1.html#T31" onmouseover="rs('finseq_1/T31')" onmouseout="rh()">FINSEQ_1:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:25"/>
<font color="Maroon" title="c3">S1</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E5:25"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="proofs_1.html#T3" target="_self" onmouseover="rs('proofs_1/T3')" onmouseout="rh()">Th42</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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