Logiweb aspects of lemma base(1/2)Sum(+1) in pyk

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The predefined "pyk" aspect

define pyk of lemma base(1/2)Sum(+1) as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small b unicode small a unicode small s unicode small e unicode left parenthesis unicode one unicode slash unicode two unicode right parenthesis unicode capital s unicode small u unicode small m unicode left parenthesis unicode plus sign unicode one unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma base(1/2)Sum(+1) as text unicode start of text unicode capital b unicode capital s unicode left parenthesis unicode plus sign unicode one unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma base(1/2)Sum(+1) as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma base(1/2)Sum(+1) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed lemma +1IsPositive(N) conclude not0 0 <= metavar var n end metavar + 1 imply not0 not0 0 = metavar var n end metavar + 1 cut 1rule base(1/2)Sum positive modus ponens not0 0 <= metavar var n end metavar + 1 imply not0 not0 0 = metavar var n end metavar + 1 conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) cut axiom plusAssociativity conclude metavar var m end metavar + metavar var n end metavar + 1 = metavar var m end metavar + metavar var n end metavar + 1 cut lemma sameExp modus ponens metavar var m end metavar + metavar var n end metavar + 1 = metavar var m end metavar + metavar var n end metavar + 1 conclude 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 cut lemma eqSymmetry modus ponens 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 conclude 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 cut lemma x=x+y-y conclude metavar var n end metavar = metavar var n end metavar + 1 + - 1 cut lemma sameBase(1/2)Sum second modus ponens metavar var n end metavar = metavar var n end metavar + 1 + - 1 conclude base(1/2)Sum( 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 + - 1 ) cut lemma eqSymmetry modus ponens base(1/2)Sum( 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 + - 1 ) conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) cut lemma addEquations modus ponens 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 modus ponens base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) conclude 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) cut lemma eqTransitivity modus ponens base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) modus ponens 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) end quote state proof state cache var c end expand end define