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<span class="kw">let </span><font color="Maroon" title="c1">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b3">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S</font> holds  (<font color="Olive" title="b3">I</font>,<font color="Maroon" title="c1">m</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</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">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> holds  (<font color="Olive" title="b2">I</font>,<font color="Maroon" title="c1">m</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">U</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">  for <font color="Olive" title="b1">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> holds  (<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">m</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">Phim</font> = <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">II</font> = <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>; <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="c6">I</font>,<font color="Maroon" title="c1">m</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">F</font> =  <a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E52"><span class="lab"><font color="Green" title="E40">Lm31</font></span></a></span>;<br/>
<a NAME="E2:182"/>
<font color="Maroon" title="c7">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)
 
;<br/>
<span class="kw">hence </span><a NAME="E3:182"/>
(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c1">m</font>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)
 ; <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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