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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,<a href="cqc_the1.html#K2" title="CQC_THE1:func.2">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st <font color="Olive" title="b1">f</font> <a href="cqc_the1.html#R2" title="CQC_THE1:pred.2">is_a_proof_wrt</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,<a href="cqc_the1.html#K2" title="CQC_THE1:func.2">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>; <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="cqc_the1.html#R2" title="CQC_THE1:pred.2">is_a_proof_wrt</a> <font color="Maroon" title="c1">X</font> implies  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>



<b>assume </b><a NAME="E1:28"/>
<font color="Maroon" title="c2">f</font> <a href="cqc_the1.html#R2" title="CQC_THE1:pred.2">is_a_proof_wrt</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:28"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D5" target="_self" title="CQC_THE1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E3:28"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</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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