### Nuprl Lemma : test2-cform-normalize

`∀[a,B:Top].`
`  (if a is lambda then <B[if a is lambda then 1 otherwise 2]`
`                       , B[if a = Ax then 3 otherwise if a is a pair then 3`
`                                                      otherwise if a is an integer then 3`
`                                                                else if a is an atom then 3`
`                                                                     otherwise isatom1(a;3;isatom2(a;3;4))]`
`                       > otherwise B[if a is lambda then 1 otherwise 2] ~ if a is lambda then <B[1], B[4]> otherwise B[2\000C])`

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` isatom1: `isatom1(z;a;b)` isatom2: `isatom2(z;a;b)` isatom: `if z is an atom then a otherwise b` ispair: `if z is a pair then a otherwise b` isaxiom: `if z = Ax then a otherwise b` islambda: `if z is lambda then a otherwise b` isint: isint def pair: `<a, b>` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  has-value: `(a)↓` all: `∀x:A. B[x]` member: `t ∈ T` implies: `P `` Q` or: `P ∨ Q` uall: `∀[x:A]. B[x]` top: `Top`
Lemmas referenced :  top_wf is-exception_wf has-value_wf_base has-value-implies-dec-islambda-2
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity cut sqequalSqle divergentSqle callbyvalueIslambda sqequalHypSubstitution sqequalTransitivity computationStep hypothesis lemma_by_obid dependent_functionElimination thin hypothesisEquality independent_functionElimination unionElimination sqleReflexivity isectElimination baseApply closedConclusion baseClosed lambdaFormation isect_memberEquality voidElimination voidEquality because_Cache introduction islambdaExceptionCases axiomSqleEquality exceptionSqequal isect_memberFormation sqequalAxiom

Latex:
\mforall{}[a,B:Top].
(if  a  is  lambda  then  <B[if  a  is  lambda  then  1  otherwise  2]
,  B[if  a  =  Ax  then  3
otherwise  if  a  is  a  pair  then  3
otherwise  if  a  is  an  integer  then  3
else  if  a  is  an  atom  then  3
otherwise  isatom1(a;3;isatom2(a;3;4))]
>  otherwise  B[if  a  is  lambda  then  1  otherwise  2]  \msim{}  if  a  is  lambda  then  <B[1],\000C  B[4]>  otherwise  B[2])

Date html generated: 2016_05_13-PM-04_08_09
Last ObjectModification: 2016_01_14-PM-07_46_24

Theory : fun_1

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