Logiweb aspects of lemma y-(1/2)(x+y)=(1/2)(y-x) in pyk

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The predefined "pyk" aspect

define pyk of lemma y-(1/2)(x+y)=(1/2)(y-x) 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 y unicode hyphen unicode left parenthesis unicode one unicode slash unicode two unicode right parenthesis unicode left parenthesis unicode small x unicode plus sign unicode small y unicode right parenthesis unicode equal sign unicode left parenthesis unicode one unicode slash unicode two unicode right parenthesis unicode left parenthesis unicode small y unicode hyphen unicode small x unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma y-(1/2)(x+y)=(1/2)(y-x) as text unicode start of text unicode small y unicode hyphen unicode left parenthesis unicode one unicode slash unicode two unicode right parenthesis unicode left parenthesis unicode small x unicode plus sign unicode small y unicode right parenthesis unicode equal sign unicode left parenthesis unicode one unicode slash unicode two unicode right parenthesis unicode left parenthesis unicode small y unicode hyphen unicode small x 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 y-(1/2)(x+y)=(1/2)(y-x) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = 1/ 1 + 1 * metavar var y end metavar + - metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma y-(1/2)(x+y)=(1/2)(y-x) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed axiom distribution conclude 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar cut lemma eqNegated modus ponens 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar conclude - 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar cut lemma eqAdditionLeft modus ponens - 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar cut axiom plusCommutativity conclude 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar cut lemma eqNegated modus ponens 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar conclude - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = - 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar cut lemma -x-y=-(x+y) conclude - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = - 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar cut lemma eqSymmetry modus ponens - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = - 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar conclude - 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar = - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar cut lemma eqTransitivity modus ponens - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = - 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar modus ponens - 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var x end metavar = - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar conclude - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar cut lemma eqAdditionLeft modus ponens - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar cut axiom plusAssociativity conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar cut lemma eqSymmetry modus ponens metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar cut lemma (1/2)x+(1/2)x=x conclude 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var y end metavar = metavar var y end metavar cut lemma positiveToRight(Eq) modus ponens 1/ 1 + 1 * metavar var y end metavar + 1/ 1 + 1 * metavar var y end metavar = metavar var y end metavar conclude 1/ 1 + 1 * metavar var y end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar cut lemma eqSymmetry modus ponens 1/ 1 + 1 * metavar var y end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar = 1/ 1 + 1 * metavar var y end metavar cut lemma eqAddition modus ponens metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar = 1/ 1 + 1 * metavar var y end metavar conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar cut lemma distributionOut(Minus) conclude 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = 1/ 1 + 1 * metavar var y end metavar + - metavar var x end metavar cut lemma eqTransitivity6 modus ponens metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar modus ponens metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + 1/ 1 + 1 * metavar var y end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar modus ponens metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar modus ponens metavar var y end metavar + - 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar modus ponens 1/ 1 + 1 * metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar = 1/ 1 + 1 * metavar var y end metavar + - metavar var x end metavar conclude metavar var y end metavar + - 1/ 1 + 1 * metavar var x end metavar + metavar var y end metavar = 1/ 1 + 1 * metavar var y end metavar + - metavar var x end metavar end quote state proof state cache var c end expand end define