Logiweb aspects of lemma insertMiddleTerm(Numerical) in pyk

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The predefined "pyk" aspect

define pyk of lemma insertMiddleTerm(Numerical) 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 i unicode small n unicode small s unicode small e unicode small r unicode small t unicode capital m unicode small i unicode small d unicode small d unicode small l unicode small e unicode capital t unicode small e unicode small r unicode small m unicode left parenthesis unicode capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma insertMiddleTerm(Numerical) as text unicode start of text unicode small i unicode small n unicode small s unicode small e unicode small r unicode small t unicode capital m unicode small i unicode small d unicode small d unicode small l unicode small e unicode capital t unicode small e unicode small r unicode small m unicode left parenthesis unicode capital n unicode small u unicode small m unicode small e unicode small r unicode small i unicode small c unicode small a unicode small l 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 insertMiddleTerm(Numerical) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) <= if( 0 <= metavar var x end metavar + - metavar var z end metavar , metavar var x end metavar + - metavar var z end metavar , - metavar var x end metavar + - metavar var z end metavar ) + if( 0 <= metavar var z end metavar + metavar var y end metavar , metavar var z end metavar + metavar var y end metavar , - metavar var z end metavar + metavar var y end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma insertMiddleTerm(Numerical) 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 all metavar var z end metavar indeed lemma splitNumericalSum conclude if( 0 <= metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , - metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar ) <= if( 0 <= metavar var x end metavar + - metavar var z end metavar , metavar var x end metavar + - metavar var z end metavar , - metavar var x end metavar + - metavar var z end metavar ) + if( 0 <= metavar var z end metavar + metavar var y end metavar , metavar var z end metavar + metavar var y end metavar , - metavar var z end metavar + metavar var y end metavar ) cut lemma insertMiddleTerm(Sum) conclude metavar var x end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar cut lemma sameNumerical modus ponens metavar var x end metavar + metavar var y end metavar = metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar conclude if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) = if( 0 <= metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , - metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar ) cut lemma eqSymmetry modus ponens if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) = if( 0 <= metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , - metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar ) conclude if( 0 <= metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , - metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar ) = if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) cut lemma subLeqLeft modus ponens if( 0 <= metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , - metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar ) = if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) modus ponens if( 0 <= metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar , - metavar var x end metavar + - metavar var z end metavar + metavar var z end metavar + metavar var y end metavar ) <= if( 0 <= metavar var x end metavar + - metavar var z end metavar , metavar var x end metavar + - metavar var z end metavar , - metavar var x end metavar + - metavar var z end metavar ) + if( 0 <= metavar var z end metavar + metavar var y end metavar , metavar var z end metavar + metavar var y end metavar , - metavar var z end metavar + metavar var y end metavar ) conclude if( 0 <= metavar var x end metavar + metavar var y end metavar , metavar var x end metavar + metavar var y end metavar , - metavar var x end metavar + metavar var y end metavar ) <= if( 0 <= metavar var x end metavar + - metavar var z end metavar , metavar var x end metavar + - metavar var z end metavar , - metavar var x end metavar + - metavar var z end metavar ) + if( 0 <= metavar var z end metavar + metavar var y end metavar , metavar var z end metavar + metavar var y end metavar , - metavar var z end metavar + metavar var y end metavar ) end quote state proof state cache var c end expand end define