Nuprl Lemma : decide-atom-if-has-value
∀t:Base. ((t)↓ ⇒ Dec(t ∈ Atom))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
decidable: Dec(P),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
base: Base,
atom: Atom
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
has-value: (a)↓,
uall: ∀[x:A]. B[x],
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
top: Top,
not: ¬A,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
bfalse: ff,
false: False
Lemmas referenced :
base_wf,
top_wf,
member_wf,
not_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
isatomCases,
divergentSqle,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
hypothesisEquality,
sqequalRule,
isatomReduceTrue,
equalityTransitivity,
equalitySymmetry,
inlEquality,
axiomEquality,
atomEquality,
isect_memberFormation,
sqequalAxiom,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
inrEquality,
lambdaEquality,
natural_numberEquality
Latex:
\mforall{}t:Base. ((t)\mdownarrow{} {}\mRightarrow{} Dec(t \mmember{} Atom))
Date html generated:
2016_05_13-PM-03_22_20
Last ObjectModification:
2016_01_14-PM-06_47_16
Theory : call!by!value_1
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