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<span class="kw">let </span><font color="Maroon" title="c3">it1</font>, <font color="Maroon" title="c4">it2</font> be   <a href="extpro_1.html#V1" title="EXTPRO_1:attr.1">strict</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> over <font color="Maroon" title="c2">N</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"> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp;  the <a href="memstr_0.html#U2" title="MEMSTR_0:sel.2">ValuesF</a> of <font color="Maroon" title="c3">it1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">N</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> &amp;  ex <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span> st <br/>( (  for <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span> holds  <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> ) &amp;  the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span></span>)</span></span>)</span> ) &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp;  the <a href="memstr_0.html#U2" title="MEMSTR_0:sel.2">ValuesF</a> of <font color="Maroon" title="c4">it2</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">N</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> &amp;  ex <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span> st <br/>( (  for <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span> holds  <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> ) &amp;  the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span></span>)</span></span>)</span> ) implies <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:15_1_2"/><span class="lab"><font color="Green" title="E6">A13</font></span>: 
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <span class="kw">and </span><br/><a NAME="E2:15_1_2"/><span class="lab"><font color="Green" title="E7">A14</font></span>: 
 the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 <span class="kw">and </span><br/><a NAME="E3:15_1_2"/><span class="lab"><font color="Green" title="E8">A15</font></span>: 
 the <a href="memstr_0.html#U2" title="MEMSTR_0:sel.2">ValuesF</a> of <font color="Maroon" title="c3">it1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">N</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span>  holds <br/>(  ex <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span> st  not <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> or  not  the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span></span>)</span></span>)</span> ) or  not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or  not  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  not  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> or  not  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> or  not  the <a href="memstr_0.html#U2" title="MEMSTR_0:sel.2">ValuesF</a> of <font color="Maroon" title="c4">it2</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">N</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> or  for <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>  holds <br/>(  ex <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span> st  not <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> or  not  the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span></span>)</span></span>)</span> ) or <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c5">f1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span><span class="kw"> such that </span><a NAME="E5:15_1_2"/><span class="lab"><font color="Green" title="E9">A16</font></span>: 
 for <font color="Olive" title="b1">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span> holds  <font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:15_1_2"/><span class="lab"><font color="Green" title="E10">A17</font></span>: 
 the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span></span>)</span></span>)</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"> (  not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or  not  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  not  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> or  not  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> or  not  the <a href="memstr_0.html#U2" title="MEMSTR_0:sel.2">ValuesF</a> of <font color="Maroon" title="c4">it2</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">N</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> or  for <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>  holds <br/>(  ex <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span> st  not <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> or  not  the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span></span>)</span></span>)</span> ) or <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E7:15_1_2"/><span class="lab"><font color="Green" title="E11">A18</font></span>: 
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <span class="kw">and </span><br/><a NAME="E8:15_1_2"/><span class="lab"><font color="Green" title="E12">A19</font></span>: 
 the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 <span class="kw">and </span><br/><a NAME="E9:15_1_2"/><span class="lab"><font color="Green" title="E13">A20</font></span>: 
 the <a href="memstr_0.html#U2" title="MEMSTR_0:sel.2">ValuesF</a> of <font color="Maroon" title="c4">it2</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">N</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>  holds <br/>(  ex <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span> st  not <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> or  not  the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span></span>)</span></span>)</span> ) or <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c6">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span><span class="kw"> such that </span><a NAME="E11:15_1_2"/><span class="lab"><font color="Green" title="E14">A21</font></span>: 
 for <font color="Olive" title="b1">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span> holds  <font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E12:15_1_2"/><span class="lab"><font color="Green" title="E15">A22</font></span>: 
 the <a href="extpro_1.html#U1" title="EXTPRO_1:sel.1">Execution</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c6">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span></span>)</span></span>)</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"> <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font></span><br/>

<a NAME="E13:15_1_2"/><span class="lab"><font color="Green" title="E16">A23</font></span>: 
 <a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c4">it2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1_2"><span class="lab"><font color="Green" title="E7">A14</font></span></a>, <a class="txt" href="#E3:15_1_2"><span class="lab"><font color="Green" title="E8">A15</font></span></a>, <a class="txt" href="#E8:15_1_2"><span class="lab"><font color="Green" title="E12">A19</font></span></a>, <a class="txt" href="#E9:15_1_2"><span class="lab"><font color="Green" title="E13">A20</font></span></a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><span class="kw">now </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">  for <font color="Olive" title="b1">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</span> holds  <font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K2" title="MEMSTR_0:func.2">the_Values_of</a> <font color="Maroon" title="c3">it1</font></span>)</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"> <font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">c</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">c</font> = 
<font color="Maroon" title="c7">c</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1_2"><span class="lab"><font color="Green" title="E9">A16</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:15_1_2"><span class="lab"><font color="Green" title="E14">A21</font></span></a>, <a class="txt" href="#E13:15_1_2"><span class="lab"><font color="Green" title="E16">A23</font></span></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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E15:15_1_2"/>
<font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1_2"><span class="lab"><font color="Green" title="E6">A13</font></span></a>, <a class="txt" href="#E2:15_1_2"><span class="lab"><font color="Green" title="E7">A14</font></span></a>, <a class="txt" href="#E6:15_1_2"><span class="lab"><font color="Green" title="E10">A17</font></span></a>, <a class="txt" href="#E7:15_1_2"><span class="lab"><font color="Green" title="E11">A18</font></span></a>, <a class="txt" href="#E8:15_1_2"><span class="lab"><font color="Green" title="E12">A19</font></span></a>, <a class="txt" href="#E12:15_1_2"><span class="lab"><font color="Green" title="E15">A22</font></span></a>, <a class="txt" href="#E3:15_1_2"><span class="lab"><font color="Green" title="E8">A15</font></span></a>, <a class="txt" href="#E9:15_1_2"><span class="lab"><font color="Green" title="E13">A20</font></span></a>, <a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</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/>


</div>
