Nuprl Lemma : has-value-implies-dec-isatom2
∀t,a,b:Base.  ((t)↓ 
⇒ ((t ∈ Atom2) ∨ (isatom2(t;a;b) ~ b)))
Proof
Definitions occuring in Statement : 
has-value: (a)↓
, 
atom: Atom$n
, 
isatom2: isatom2(z;a;b)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
, 
member: t ∈ T
, 
base: Base
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
has-value: (a)↓
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
or: P ∨ Q
, 
top: Top
, 
guard: {T}
, 
prop: ℙ
Lemmas referenced : 
base_wf, 
equal-wf-base, 
top_wf, 
is-exception_wf, 
has-value_wf_base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
isatom2Cases, 
divergentSqle, 
hypothesis, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
baseClosed, 
hypothesisEquality, 
sqequalRule, 
isAtom2ReduceTrue, 
equalityTransitivity, 
equalitySymmetry, 
inlFormation, 
because_Cache, 
sqequalIntensionalEquality, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
inrFormation, 
atomnEquality
Latex:
\mforall{}t,a,b:Base.    ((t)\mdownarrow{}  {}\mRightarrow{}  ((t  \mmember{}  Atom2)  \mvee{}  (isatom2(t;a;b)  \msim{}  b)))
Date html generated:
2016_05_13-PM-03_22_56
Last ObjectModification:
2016_01_14-PM-06_46_30
Theory : call!by!value_1
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