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<span class="kw">let </span><font color="Maroon" title="c1">P</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">m1</font>, <font color="Olive" title="b2">m2</font> being   <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Maroon" title="c1">P</font> holds  <font color="Olive" title="b1">m1</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Olive" title="b1">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Olive" title="b2">m2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">m1</font>, <font color="Maroon" title="c3">m2</font> be   <a href="pnproc_1.html#NM1" title="PNPROC_1:NM.1">marking</a> of <font color="Maroon" title="c1">P</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"> <font color="Maroon" title="c2">m1</font> <a href="pnproc_1.html#R2" title="PNPROC_1:pred.2">c=</a> <font color="Maroon" title="c2">m1</font> <a href="pnproc_1.html#K2" title="PNPROC_1:func.2">+</a> <font color="Maroon" title="c3">m2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pnproc_1.html#D3" target="_self" onmouseover="rs('pnproc_1/D3')" onmouseout="rh()">PNPROC_1:def 3</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="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">P</font> implies <font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:11"/>
<font color="Maroon" title="c4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">P</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"> <font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span><br/>

<a NAME="E2:11"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#D4" target="_self" onmouseover="rs('pnproc_1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:11"/>
<font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">p</font> <a href="pnproc_1.html#NK1" title="PNPROC_1:NK.1">multitude_of</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</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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