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<span class="kw">let </span><font color="Maroon" title="c1">Al</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</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">p</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b2">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b3">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b4">S</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>  st <font color="Olive" title="b4">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Olive" title="b2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<font color="Olive" title="b3">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> &amp; <font color="Olive" title="b4">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> holds <br/>( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b4">S</font>,<font color="Olive" title="b2">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  &amp;  ex <font color="Olive" title="b5">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b5">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</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">  for <font color="Olive" title="b1">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b2">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b3">S</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>  st <font color="Olive" title="b3">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Olive" title="b1">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b2">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b2">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> &amp; <font color="Olive" title="b3">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> holds <br/>( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b3">S</font>,<font color="Olive" title="b1">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  &amp;  ex <font color="Olive" title="b4">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b4">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b2">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</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">  for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font><br/>  for <font color="Olive" title="b2">S</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>  st <font color="Olive" title="b2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b1">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> holds <br/>( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b2">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  &amp;  ex <font color="Olive" title="b3">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</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">  for <font color="Olive" title="b1">S</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>  st <font color="Olive" title="b1">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> &amp; <font color="Olive" title="b1">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> holds <br/>( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  &amp;  ex <font color="Olive" title="b2">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b2">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</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="c5">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> implies ( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  &amp;  ex <font color="Olive" title="b1">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> ) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">Sub1</font> = <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">Sub</font> = <font color="Maroon" title="c4">Sub</font> as   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> ;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:11"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c5">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:11"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c5">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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"> ( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  &amp;  ex <font color="Olive" title="b1">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> )</span><br/>

<a NAME="E4:11"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
( <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> <a href="sublemma.html#K8" title="SUBLEMMA:func.8">`1</a></span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E12">A2</font></span></a></span>;<br/>
<a NAME="E5:11"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
(  <a href="qc_lang1.html#K22" title="QC_LANG1:func.22">the_scope_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> &amp;  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>) is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D21" onmouseover="rs('qc_lang1/D21')" onmouseout="rh()">QC_LANG1:def 21</a>, <a class="ref" href="qc_lang2.html#T7" onmouseover="rs('qc_lang2/T7')" onmouseout="rh()">QC_LANG2:7</a></span>;<br/>
<a NAME="E6:11"/>
( <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c7">Sub</font>)</span>)</span>) &amp;  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T9" target="_self" onmouseover="rs('substut2/T9')" onmouseout="rh()">Th9</a>, <a class="ref" href="qc_lang2.html#T7" onmouseover="rs('qc_lang2/T7')" onmouseout="rh()">QC_LANG2:7</a></span>;<br/>
<a NAME="E7:11"/><span class="kw">then </span>
 <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>),<font color="Maroon" title="c7">Sub</font> <a href="substut1.html#R1" title="SUBSTUT1:pred.1">PQSub</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:11"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="substut1.html#D14" onmouseover="rs('substut1/D14')" onmouseout="rh()">SUBSTUT1:def 14</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E9:11"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c7">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p4">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p5">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p4">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p5"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">and </span><br/><a NAME="E10:11"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
 <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>),<font color="Maroon" title="c7">Sub</font> <a href="substut1.html#R1" title="SUBSTUT1:pred.1">PQSub</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 ;<br/>
<a NAME="E11:11"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:11"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E10:11"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="ref" href="substut1.html#D15" onmouseover="rs('substut1/D15')" onmouseout="rh()">SUBSTUT1:def 15</a></span>;<br/>
<a NAME="E12:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<span class="p1">(<span class="default"><a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c7">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:11"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="funct_1.html#T1" onmouseover="rs('funct_1/T1')" onmouseout="rh()">FUNCT_1:1</a></span>;<br/>
<a NAME="E13:11"/><span class="lab"><font color="Green" title="E18">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> <a href="sublemma.html#K8" title="SUBLEMMA:func.8">`1</a></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font>)</span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:11"/>
<span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:11"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="substut1.html#D22" onmouseover="rs('substut1/D22')" onmouseout="rh()">SUBSTUT1:def 22</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">  ex <font color="Olive" title="b1">S1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span><br/>

<a NAME="E15:11"/><span class="lab"><font color="Green" title="E19">A9</font></span>: 
<span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:11"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="substut1.html#D22" onmouseover="rs('substut1/D22')" onmouseout="rh()">SUBSTUT1:def 22</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">Sub</font> = <font color="Maroon" title="c7">Sub</font> as    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:11"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="substut1.html#D23" onmouseover="rs('substut1/D23')" onmouseout="rh()">SUBSTUT1:def 23</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c10">S1</font> =  <a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span>,<font color="Maroon" title="c9">Sub</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="c10">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span><br/>

<a NAME="E17:11"/>
<font color="Maroon" title="c10">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> (<span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c3">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span>,<font color="Maroon" title="c9">Sub</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="ref" href="sublemma.html#D5" onmouseover="rs('sublemma/D5')" onmouseout="rh()">SUBLEMMA:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:11"/>
<font color="Maroon" title="c10">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="ref" href="substut1.html#D24" onmouseover="rs('substut1/D24')" onmouseout="rh()">SUBSTUT1:def 24</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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