Nuprl Lemma : evalall-is-exception
∀[x,u,v:Base]. ((evalall(x) ~ exception(u; v)) ⇒ (↓(x ~ exception(u; v)) ∨ (x)↓))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
evalall: evalall(t),
uall: ∀[x:A]. B[x],
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
evalall: evalall(t),
is-exception: is-exception(t),
not: ¬A,
false: False,
guard: {T},
or: P ∨ Q,
squash: ↓T,
prop: ℙ
Lemmas referenced :
base_wf,
is-exception_wf,
has-value_wf_base,
exception-not-bottom,
bottom_diverge
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
sqleRule,
divergentSqle,
lemma_by_obid,
independent_functionElimination,
thin,
voidElimination,
isectElimination,
baseClosed,
because_Cache,
callbyvalueExceptionCases,
inrFormation,
sqequalIntensionalEquality,
hypothesisEquality,
baseApply,
closedConclusion,
imageMemberEquality,
imageElimination,
exceptionSqequal,
addLevel,
rename,
inlFormation,
levelHypothesis,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[x,u,v:Base]. ((evalall(x) \msim{} exception(u; v)) {}\mRightarrow{} (\mdownarrow{}(x \msim{} exception(u; v)) \mvee{} (x)\mdownarrow{}))
Date html generated:
2016_05_13-PM-03_28_39
Last ObjectModification:
2016_01_14-PM-06_42_08
Theory : arithmetic
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