Nuprl Lemma : partial-not-exception
∀[T:Type]. ∀[x:partial(T)].  (¬is-exception(x))
Proof
Definitions occuring in Statement : 
partial: partial(T)
, 
is-exception: is-exception(t)
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
universe: Type
Definitions unfolded in proof : 
prop: ℙ
, 
and: P ∧ Q
, 
quotient: x,y:A//B[x; y]
, 
partial: partial(T)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
squash: ↓T
, 
is-exception: is-exception(t)
, 
rev_implies: P 
⇐ Q
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
iff: P 
⇐⇒ Q
, 
true: True
Lemmas referenced : 
is-exception_wf, 
base-partial-not-exception, 
not_wf, 
squash_wf, 
true_wf, 
equal-wf-base, 
base-partial_wf, 
per-partial_wf, 
partial_wf
Rules used in proof : 
universeEquality, 
cumulativity, 
because_Cache, 
hypothesisEquality, 
isectElimination, 
lemma_by_obid, 
productEquality, 
hypothesis, 
thin, 
productElimination, 
cut, 
pertypeElimination, 
sqequalRule, 
pointwiseFunctionalityForEquality, 
sqequalHypSubstitution, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
baseClosed, 
imageMemberEquality, 
equalitySymmetry, 
equalityTransitivity, 
imageElimination, 
lambdaEquality, 
applyEquality, 
sqleExtensionalEquality, 
voidElimination, 
independent_functionElimination, 
lambdaFormation, 
independent_pairFormation, 
natural_numberEquality
Latex:
\mforall{}[T:Type].  \mforall{}[x:partial(T)].    (\mneg{}is-exception(x))
Date html generated:
2019_06_20-PM-00_33_43
Last ObjectModification:
2018_10_15-PM-09_42_01
Theory : partial_1
Home
Index