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<b>let </b><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">F</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V8" title="ZF_LANG:attr.8">disjunctive</a> implies ( ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> implies  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; (  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> implies  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Olive" title="b1">G</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; (  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Olive" title="b1">G</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> ) ) )</span><br/>



<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V8" title="ZF_LANG:attr.8">disjunctive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> implies  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; (  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> implies  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Olive" title="b1">G</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; (  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Olive" title="b1">G</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> ) )</span><br/>

<b>then consider </b><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><b> such that </b><br/><a NAME="E3:54"/><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D20" target="_self" title="ZF_LANG:def.20">Def20</a></i>;<br/>
<a NAME="E4:54"/>
<font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="txt" href="#E3:54"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>;<br/>
<a NAME="E5:54"/><b>then </b>
not <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V5" title="ZF_LANG:attr.5">conjunctive</a>
 
<b>by </b><i><a class="ref" href="zf_lang.html#T38" target="_self" title="ZF_LANG:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E6:54"/>
( ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> implies  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; (  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Maroon" title="c2">F</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> implies  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Olive" title="b1">G</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> ) &amp; (  ex <font color="Olive" title="b1">G</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> st <font color="Olive" title="b1">G</font> <a href="zf_lang.html#K10" title="ZF_LANG:func.10">'or'</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> ) )
 <b>by </b><i><a class="txt" href="#E1:54"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="zf_lang.html#D31" target="_self" title="ZF_LANG:def.31">Def31</a>, <a class="ref" href="zf_lang.html#D32" target="_self" title="ZF_LANG:def.32">Def32</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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