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

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The predefined "pyk" aspect

define pyk of lemma base(1/2)Sum bound 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 b unicode small o unicode small u unicode small n unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma base(1/2)Sum bound 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 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 bound as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed not0 base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) <= 1/ 1 + 1 ^ metavar var m end metavar imply not0 not0 base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) = 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 bound 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 base(1/2)Sum exact bound 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 cut axiom plusCommutativity conclude 1/ 1 + 1 ^ 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 ) = 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 eqTransitivity modus ponens 1/ 1 + 1 ^ 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 ) = 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 1/ 1 + 1 ^ 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 cut lemma positiveToRight(Eq) modus ponens 1/ 1 + 1 ^ 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 conclude 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar + - base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) cut lemma 0<1/2 conclude not0 0 <= 1/ 1 + 1 imply not0 not0 0 = 1/ 1 + 1 cut lemma positiveBase modus ponens not0 0 <= 1/ 1 + 1 imply not0 not0 0 = 1/ 1 + 1 conclude not0 0 <= 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar imply not0 not0 0 = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar cut lemma subLessRight modus ponens 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar = 1/ 1 + 1 ^ metavar var m end metavar + - base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) modus ponens not0 0 <= 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar imply not0 not0 0 = 1/ 1 + 1 ^ metavar var m end metavar + 1 + metavar var n end metavar conclude not0 0 <= 1/ 1 + 1 ^ metavar var m end metavar + - base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) imply not0 not0 0 = 1/ 1 + 1 ^ metavar var m end metavar + - base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) cut lemma negativeToLeft(Less)(1 term) modus ponens not0 0 <= 1/ 1 + 1 ^ metavar var m end metavar + - base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) imply not0 not0 0 = 1/ 1 + 1 ^ metavar var m end metavar + - base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) conclude not0 base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) <= 1/ 1 + 1 ^ metavar var m end metavar imply not0 not0 base(1/2)Sum( metavar var m end metavar + 1 , metavar var n end metavar ) = 1/ 1 + 1 ^ metavar var m end metavar end quote state proof state cache var c end expand end define