Nuprl Lemma : atomic-values-evalall
∀[x:Base]. (evalall(x))↓ supposing x ∈ atomic-values()
Proof
Definitions occuring in Statement :
atomic-values: atomic-values(),
has-value: (a)↓,
evalall: evalall(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
atomic-values: atomic-values(),
Value: Value(),
is-atomic: is-atomic(x),
evalall: evalall(t),
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
top: Top,
outl: outl(x),
outr: outr(x),
btrue: tt
Lemmas referenced :
equal-wf-base,
atomic-values_wf,
base_wf,
equal_wf,
has-value-implies-dec-ispair-2,
top_wf,
has-value-implies-dec-isinl-2,
has-value-implies-dec-isinr-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomSqleEquality,
hypothesis,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
setElimination,
rename,
dependent_functionElimination,
independent_functionElimination,
callbyvalueReduce,
unionElimination,
voidElimination,
voidEquality
Latex:
\mforall{}[x:Base]. (evalall(x))\mdownarrow{} supposing x \mmember{} atomic-values()
Date html generated:
2017_04_17-AM-09_07_26
Last ObjectModification:
2017_02_27-PM-05_14_59
Theory : rec_values
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