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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