Logiweb aspects of system Q in pyk

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The predefined "pyk" aspect

define pyk of system Q as text unicode start of text unicode small s unicode small y unicode small s unicode small t unicode small e unicode small m unicode space unicode capital q unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of system Q as text unicode start of text unicode capital s unicode small y unicode small s unicode small t unicode small e unicode small m unicode capital q unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of system Q as all metavar var fx end metavar indeed all metavar var fy end metavar indeed R( metavar var fx end metavar ) ++ R( metavar var fy end metavar ) == R( metavar var fy end metavar ) ++ R( metavar var fx end metavar ) rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) ** R( metavar var fz end metavar ) == R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) ** R( metavar var fz end metavar ) rule plus all metavar var fx end metavar indeed all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar == metavar var ry end metavar infer metavar var fx end metavar in0 metavar var rx end metavar infer metavar var fx end metavar in0 metavar var ry end metavar rule plus all metavar var m end metavar indeed upperBound( 01//02 ** [ xs ; metavar var m end metavar ] ++ [ us ; metavar var m end metavar ] , setOfReals ) infer [ xs ; metavar var m end metavar + 1 ] == [ xs ; metavar var m end metavar ] rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar imply metavar var x end metavar = metavar var y end metavar rule plus all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var s end metavar in0 zermelo pair metavar var x end metavar comma metavar var y end metavar end pair imply not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply not0 not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar in0 zermelo pair metavar var x end metavar comma metavar var y end metavar end pair rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed metavar var n end metavar = 0 infer base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) = 1/ 1 + 1 ^ metavar var m end metavar rule plus all metavar var x end metavar indeed metavar var x end metavar + 0 = metavar var x end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed R( metavar var fx end metavar ) == R( metavar var fy end metavar ) infer metavar var fx end metavar sameF metavar var fy end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar <= metavar var y end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar imply metavar var b end metavar infer metavar var a end metavar infer metavar var b end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar ) = R( metavar var fy end metavar ) infer R( metavar var fx end metavar ) ++ R( metavar var fz end metavar ) = R( metavar var fy end metavar ) ++ R( metavar var fz end metavar ) rule plus all metavar var fx end metavar indeed R( metavar var fx end metavar ) ++ R( 0f ) == R( metavar var fx end metavar ) rule plus all metavar var x end metavar indeed metavar var x end metavar * 1 = metavar var x end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer metavar var b end metavar rule plus all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar == metavar var ry end metavar infer metavar var ry end metavar == metavar var rx end metavar rule plus all metavar var m end metavar indeed all metavar var x end metavar indeed metavar var m end metavar = 0 infer metavar var x end metavar ^ metavar var m end metavar = 1 rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 0 <= metavar var z end metavar imply metavar var x end metavar <= metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar rule plus all metavar var fx end metavar indeed R( metavar var fx end metavar ) ** R( 1f ) == R( metavar var fx end metavar ) rule plus not0 0 = 1 rule plus all metavar var m end metavar indeed Nat( metavar var m end metavar ) endorse 0 <= metavar var m end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar zermelo is metavar var y end metavar imply for all objects object var var s end var indeed not0 object var var s end var in0 metavar var x end metavar imply object var var s end var in0 metavar var y end metavar imply not0 object var var s end var in0 metavar var y end metavar imply object var var s end var in0 metavar var x end metavar imply not0 for all objects object var var s end var indeed not0 object var var s end var in0 metavar var x end metavar imply object var var s end var in0 metavar var y end metavar imply not0 object var var s end var in0 metavar var y end metavar imply object var var s end var in0 metavar var x end metavar imply metavar var x end metavar zermelo is metavar var y end metavar rule plus all metavar var rx end metavar indeed all metavar var ry end metavar indeed all metavar var rz end metavar indeed metavar var rx end metavar == metavar var ry end metavar infer metavar var ry end metavar == metavar var rz end metavar infer metavar var rx end metavar == metavar var rz end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar + metavar var y end metavar = metavar var y end metavar + metavar var x end metavar rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed [ metavar var fx end metavar +f metavar var fy end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] rule plus all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed meta-sub metavar var b end metavar is metavar var a end metavar where metavar var v1 end metavar is 0 end sub endorse meta-sub metavar var c end metavar is metavar var a end metavar where metavar var v1 end metavar is metavar var v1 end metavar + 1 end sub endorse metavar var b end metavar imply for all objects metavar var v1 end metavar indeed metavar var a end metavar imply metavar var c end metavar imply for all objects metavar var v1 end metavar indeed metavar var a end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed metavar var n end metavar = 0 infer UStelescope( metavar var m end metavar , metavar var n end metavar ) = | [ us ; metavar var m end metavar ] + - [ us ; metavar var m end metavar + 1 ] | rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar ) ++ R( metavar var fy end metavar ) ++ R( metavar var fz end metavar ) = R( metavar var fx end metavar ) ++ R( metavar var fy end metavar ) ++ R( metavar var fz end metavar ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar * metavar var y end metavar = metavar var y end metavar * metavar var x end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar in0 R( metavar var fy end metavar ) infer metavar var fx end metavar sameF metavar var fy end metavar rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar rule plus all metavar var a end metavar indeed metavar var a end metavar infer metavar var a end metavar rule plus all metavar var m end metavar indeed upperBound( 01//02 ** [ xs ; metavar var m end metavar ] ++ [ us ; metavar var m end metavar ] , setOfReals ) infer [ us ; metavar var m end metavar + 1 ] == 01//02 ** [ xs ; metavar var m end metavar ] ++ [ us ; metavar var m end metavar ] rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar rule plus all metavar var s end metavar indeed all metavar var x end metavar indeed not0 metavar var s end metavar in0 power metavar var x end metavar end power imply for all objects object var var s end var indeed object var var s end var in0 metavar var s end metavar imply object var var s end var in0 metavar var x end metavar imply not0 for all objects object var var s end var indeed object var var s end var in0 metavar var s end metavar imply object var var s end var in0 metavar var x end metavar imply metavar var s end metavar in0 power metavar var x end metavar end power rule plus [ us ; 0 ] == [ xs ; 0 ] ++ R( 1f ) rule plus all metavar var x end metavar indeed metavar var x end metavar <= metavar var x end metavar rule plus all metavar var s end metavar indeed not0 metavar var s end metavar in0 zermelo empty set rule plus all metavar var x end metavar indeed metavar var x end metavar + - metavar var x end metavar = 0 rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar = metavar var z end metavar imply metavar var y end metavar = metavar var z end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed not0 0 <= metavar var n end metavar imply not0 not0 0 = metavar var n end metavar infer UStelescope( metavar var m end metavar , metavar var n end metavar ) = | [ us ; metavar var m end metavar + metavar var n end metavar ] + - [ us ; metavar var m end metavar + metavar var n end metavar + 1 ] | + UStelescope( metavar var m end metavar , metavar var n end metavar + - 1 ) rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) == R( metavar var fx end metavar +f metavar var fy end metavar +f metavar var fz end metavar ) rule plus all metavar var x end metavar indeed not0 metavar var x end metavar = 0 imply metavar var x end metavar * 1/ metavar var x end metavar = 1 rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed not0 metavar var b end metavar imply metavar var a end metavar infer not0 metavar var b end metavar imply not0 metavar var a end metavar infer metavar var b end metavar rule plus all metavar var rx end metavar indeed metavar var rx end metavar == metavar var rx end metavar rule plus all metavar var m end metavar indeed not0 upperBound( 01//02 ** [ xs ; metavar var m end metavar ] ++ [ us ; metavar var m end metavar ] , setOfReals ) infer [ us ; metavar var m end metavar + 1 ] == [ us ; metavar var m end metavar ] rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar imply metavar var x end metavar + metavar var z end metavar <= metavar var y end metavar + metavar var z end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var p end metavar indeed all metavar var x end metavar indeed all metavar var z end metavar indeed metavar var p end metavar is placeholder-var and ph-sub metavar var b end metavar is metavar var a end metavar where metavar var p end metavar is metavar var z end metavar end sub endorse not0 metavar var z end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply not0 metavar var z end metavar in0 metavar var x end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var z end metavar in0 metavar var x end metavar imply not0 metavar var b end metavar imply metavar var z end metavar in0 the set of ph in metavar var x end metavar such that metavar var a end metavar end set rule plus all metavar var m end metavar indeed all metavar var fx end metavar indeed R( metavar var fx end metavar ) ++ -- R( metavar var fx end metavar ) == R( 0f ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar * metavar var y end metavar + metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * metavar var z end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed Nat( metavar var m end metavar ) endorse Nat( metavar var n end metavar ) endorse not0 metavar var m end metavar <= metavar var n end metavar + 1 imply not0 not0 metavar var m end metavar = metavar var n end metavar + 1 infer metavar var m end metavar <= metavar var n end metavar rule plus all metavar var x end metavar indeed all metavar var t end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed exist-sub0 quote metavar var a end metavar end quote is quote metavar var b end metavar end quote where quote metavar var x end metavar end quote is quote metavar var t end metavar end quote end sub endorse metavar var a end metavar infer metavar var b end metavar rule plus all metavar var m end metavar indeed all metavar var x end metavar indeed not0 0 <= metavar var m end metavar imply not0 not0 0 = metavar var m end metavar infer metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar + - 1 rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar + metavar var y end metavar + metavar var z end metavar = metavar var x end metavar + metavar var y end metavar + metavar var z end metavar rule plus all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed all metavar var n end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed for all objects metavar var ep end metavar indeed not0 for all objects metavar var n end metavar indeed not0 for all objects metavar var v1 end metavar indeed for all objects metavar var v2 end metavar indeed not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar imply metavar var n end metavar <= metavar var v1 end metavar imply metavar var n end metavar <= metavar var v2 end metavar imply not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | <= metavar var ep end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v1 end metavar ] + - [ metavar var fx end metavar ; metavar var v2 end metavar ] | = metavar var ep end metavar rule plus all metavar var x end metavar indeed all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed meta-sub metavar var a end metavar is metavar var b end metavar where metavar var v1 end metavar is metavar var x end metavar end sub endorse for all objects metavar var v1 end metavar indeed metavar var b end metavar imply metavar var a end metavar rule plus all metavar var m end metavar indeed all metavar var n end metavar indeed not0 0 <= metavar var n end metavar imply not0 not0 0 = metavar var n end metavar infer base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + - 1 ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar * metavar var y end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar * metavar var z end metavar rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed metavar var fx end metavar sameF metavar var fy end metavar infer R( metavar var fx end metavar ) == R( metavar var fy end metavar ) rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar + metavar var z end metavar = metavar var y end metavar + metavar var z end metavar rule plus all metavar var x end metavar indeed all metavar var a end metavar indeed metavar var a end metavar infer for all objects metavar var x end metavar indeed metavar var a end metavar rule plus all metavar var m end metavar indeed not0 upperBound( 01//02 ** [ xs ; metavar var m end metavar ] ++ [ us ; metavar var m end metavar ] , setOfReals ) infer [ xs ; metavar var m end metavar + 1 ] == 01//02 ** [ xs ; metavar var m end metavar ] ++ [ us ; metavar var m end metavar ] rule plus all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var z end metavar imply metavar var x end metavar <= metavar var z end metavar rule plus all metavar var s end metavar indeed all metavar var x end metavar indeed not0 metavar var s end metavar in0 union metavar var x end metavar end union imply not0 metavar var s end metavar in0 existential var var j end var imply not0 existential var var j end var in0 metavar var x end metavar imply not0 not0 metavar var s end metavar in0 existential var var j end var imply not0 existential var var j end var in0 metavar var x end metavar imply metavar var s end metavar in0 union metavar var x end metavar end union rule plus all metavar var fx end metavar indeed all metavar var fy end metavar indeed R( metavar var fx end metavar ) ** R( metavar var fy end metavar ) == R( metavar var fy end metavar ) ** R( metavar var fx end metavar ) rule plus all metavar var fx end metavar indeed all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar == metavar var ry end metavar infer metavar var fx end metavar in0 metavar var ry end metavar infer metavar var fx end metavar in0 metavar var rx end metavar end define