Logiweb aspects of lemma base(1/2)Sum exact bound indu in pyk

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The predefined "pyk" aspect

define pyk of lemma base(1/2)Sum exact bound indu 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 space unicode small e unicode small x unicode small a unicode small c unicode small t unicode space unicode small b unicode small o unicode small u unicode small n unicode small d unicode space unicode small i unicode small n unicode small d unicode small u unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma base(1/2)Sum exact bound indu as text unicode start of text unicode capital b unicode capital s unicode small b unicode small o unicode small u unicode small n unicode small d unicode left parenthesis unicode capital e unicode small x unicode small a unicode small c unicode small t unicode right parenthesis unicode left parenthesis unicode capital i unicode small n unicode small d unicode small u 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 exact bound indu 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 + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar imply base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma base(1/2)Sum exact bound indu 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 base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar infer lemma base(1/2)Sum(+1) conclude base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) cut lemma eqAddition modus ponens base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) conclude base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 cut axiom plusCommutativity conclude 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) = base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 cut lemma eqAddition modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) = base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 conclude 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 cut lemma exp(+1) conclude 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar cut lemma addEquations modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar conclude 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar cut lemma (1/2)x+(1/2)x=x conclude 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar cut lemma eqTransitivity modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar modus ponens 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1/ 1 + 1 * 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar conclude 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar cut lemma three2twoTerms modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar conclude base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar cut lemma eqTransitivity5 modus ponens base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 modus ponens base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar modus ponens base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar conclude base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar cut all metavar var m end metavar indeed all metavar var n end metavar indeed 1rule deduction modus ponens all metavar var m end metavar indeed all metavar var n end metavar indeed base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar infer base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar conclude base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar imply base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar + 1 ) + 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar end quote state proof state cache var c end expand end define