### Nuprl Lemma : test4-cform-normalize

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

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` 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` not: `¬A` false: `False` top: `Top` uall: `∀[x:A]. B[x]`
Lemmas referenced :  not-atom-member-int has-value-implies-dec-isatom-2 has-value-implies-dec-islambda-2 has-value-implies-dec-ispair-2 is-exception_wf has-value_wf_base top_wf not-btrue-sqeq-bfalse has-value-implies-dec-isaxiom-2 has-value-implies-dec-isint-2
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity cut sqequalSqle divergentSqle callbyvalueIsint sqequalHypSubstitution sqequalTransitivity computationStep hypothesis lemma_by_obid dependent_functionElimination thin hypothesisEquality independent_functionElimination unionElimination isintReduceTrue equalityTransitivity equalitySymmetry sqleRule sqleReflexivity because_Cache voidElimination lambdaFormation isect_memberEquality voidEquality isectElimination baseApply closedConclusion baseClosed introduction isintExceptionCases axiomSqleEquality exceptionSqequal isect_memberFormation sqequalAxiom

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

Date html generated: 2016_05_13-PM-04_08_13
Last ObjectModification: 2016_01_14-PM-07_46_32

Theory : fun_1

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