Nuprl Lemma : is-exception-evalall
∀[x:Base]. (is-exception(evalall(x)) 
⇒ (↓is-exception(x) ∨ (x)↓))
Proof
Definitions occuring in Statement : 
has-value: (a)↓
, 
is-exception: is-exception(t)
, 
evalall: evalall(t)
, 
uall: ∀[x:A]. B[x]
, 
squash: ↓T
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
, 
base: Base
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
or: P ∨ Q
, 
prop: ℙ
, 
guard: {T}
, 
is-exception: is-exception(t)
, 
not: ¬A
, 
false: False
Lemmas referenced : 
exception-not-bottom, 
bottom_diverge, 
base_wf, 
is-exception_wf, 
has-value_wf_base, 
evalall-is-exception
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaFormation, 
exceptionSqequal, 
hypothesis, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
independent_functionElimination, 
imageElimination, 
unionElimination, 
inlFormation, 
sqequalRule, 
inrFormation, 
imageMemberEquality, 
baseClosed, 
baseApply, 
closedConclusion, 
lambdaEquality, 
dependent_functionElimination, 
divergentSqle, 
sqleRule, 
voidElimination, 
because_Cache
Latex:
\mforall{}[x:Base].  (is-exception(evalall(x))  {}\mRightarrow{}  (\mdownarrow{}is-exception(x)  \mvee{}  (x)\mdownarrow{}))
Date html generated:
2016_05_13-PM-03_28_39
Last ObjectModification:
2016_01_14-PM-06_41_59
Theory : arithmetic
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