Nuprl Lemma : bnot-wf-partial
∀[b:partial(Base)]. (¬bb ∈ partial(𝔹))
Proof
Definitions occuring in Statement :
partial: partial(T),
bnot: ¬bb,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bool: 𝔹,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
not: ¬A,
prop: ℙ,
squash: ↓T,
false: False
Lemmas referenced :
base-member-partial,
bool_wf,
union-value-type,
unit_wf2,
partial_subtype_base,
base_wf,
subtype_rel_self,
has-value-bnot-type,
bfalse_wf,
btrue_wf,
is-exception_wf,
partial_wf,
exception-not-value,
bool_subtype_base,
value-type-has-value,
partial-not-exception
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
Error :equalityIsType1,
axiomEquality,
Error :universeIsType,
decideExceptionCases,
imageElimination,
imageMemberEquality,
voidElimination
Latex:
\mforall{}[b:partial(Base)]. (\mneg{}\msubb{}b \mmember{} partial(\mBbbB{}))
Date html generated:
2019_06_20-PM-00_34_25
Last ObjectModification:
2018_10_18-PM-02_50_20
Theory : partial_1
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