Nuprl Lemma : base-partial-not-exception
∀[T:Type]. ∀[x:base-partial(T)]. (¬is-exception(x))
Proof
Definitions occuring in Statement :
base-partial: base-partial(T),
is-exception: is-exception(t),
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
base-partial: base-partial(T),
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
is-exception_wf,
base-partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
setElimination,
rename,
productElimination,
hypothesis,
independent_functionElimination,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:base-partial(T)]. (\mneg{}is-exception(x))
Date html generated:
2016_05_14-AM-06_09_20
Last ObjectModification:
2015_12_26-AM-11_52_27
Theory : partial_1
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