Logiweb aspects of lemma fpart-Bounded indu in pyk

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The predefined "pyk" aspect

define pyk of lemma fpart-Bounded 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 f unicode small p unicode small a unicode small r unicode small t unicode hyphen unicode capital b unicode small o unicode small u unicode small n unicode small d unicode small e 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 fpart-Bounded indu as text unicode start of text unicode capital f unicode small p unicode small a unicode small r unicode small t unicode hyphen unicode capital b unicode small o unicode small u unicode small n unicode small d unicode small e unicode small d 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 fpart-Bounded indu as system Q infer all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var n end metavar indeed all metavar var fx end metavar indeed not0 for all objects metavar var v1 end metavar indeed not0 for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar + 1 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fpart-Bounded indu as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var n end metavar indeed all metavar var fx end metavar indeed metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar infer metavar var v2n end metavar <= metavar var n end metavar + 1 infer lemma fpart-Bounded indu helper modus ponens metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar modus ponens metavar var v2n end metavar <= metavar var n end metavar + 1 conclude not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) cut all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var n end metavar indeed all metavar var fx end metavar indeed 1rule deduction modus ponens all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var n end metavar indeed all metavar var fx end metavar indeed metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar infer metavar var v2n end metavar <= metavar var n end metavar + 1 infer not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) conclude metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar imply metavar var v2n end metavar <= metavar var n end metavar + 1 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) cut pred lemma addAll modus ponens metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar imply metavar var v2n end metavar <= metavar var n end metavar + 1 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) conclude for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar imply for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar + 1 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) cut pred lemma addExist(SimpleAnt) at if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) modus ponens for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar imply for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar + 1 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = if( | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 <= metavar var v1 end metavar , metavar var v1 end metavar , | [ metavar var fx end metavar ; metavar var n end metavar + 1 ] | + 1 ) conclude not0 for all objects metavar var v1 end metavar indeed not0 for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= metavar var n end metavar + 1 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar end quote state proof state cache var c end expand end define