Nuprl Lemma : has-value-implies-dec-islambda-2
∀t:Base. ((t)↓ 
⇒ ((t ~ λx.(t x)) ∨ (∀a,b:Base.  (if t is lambda then a otherwise b ~ b))))
Proof
Definitions occuring in Statement : 
has-value: (a)↓
, 
islambda: if z is lambda then a otherwise b
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
, 
apply: f a
, 
lambda: λx.A[x]
, 
base: Base
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
or: P ∨ Q
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
guard: {T}
, 
uimplies: b supposing a
, 
has-value: (a)↓
, 
false: False
, 
top: Top
, 
sq_type: SQType(T)
Lemmas referenced : 
top_wf, 
not_zero_sqequal_one, 
is-exception_wf, 
has-value_wf_base, 
subtype_rel_self, 
subtype_base_sq, 
base_wf, 
all_wf, 
has-value-implies-dec-islambda
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
baseClosed, 
independent_functionElimination, 
hypothesis, 
unionElimination, 
inlFormation, 
isectElimination, 
sqequalRule, 
lambdaEquality, 
sqequalIntensionalEquality, 
baseApply, 
closedConclusion, 
inrFormation, 
instantiate, 
because_Cache, 
independent_isectElimination, 
islambdaCases, 
divergentSqle, 
voidElimination, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
isect_memberEquality, 
voidEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}t:Base.  ((t)\mdownarrow{}  {}\mRightarrow{}  ((t  \msim{}  \mlambda{}x.(t  x))  \mvee{}  (\mforall{}a,b:Base.    (if  t  is  lambda  then  a  otherwise  b  \msim{}  b))))
Date html generated:
2016_05_13-PM-03_22_47
Last ObjectModification:
2016_01_14-PM-06_46_38
Theory : call!by!value_1
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