Nuprl Lemma : band-wf-partial
∀[a:partial(Base)]. ∀[b:partial(𝔹)]. (a ∧b b ∈ partial(𝔹))
Proof
Definitions occuring in Statement :
partial: partial(T),
band: p ∧b q,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
band: p ∧b q,
ifthenelse: if b then t else f fi ,
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,
has-value: (a)↓,
not: ¬A,
prop: ℙ,
bfalse: ff,
squash: ↓T,
false: False
Lemmas referenced :
partial_wf,
bool_wf,
base_wf,
base-member-partial,
union-value-type,
unit_wf2,
partial_subtype_base,
bool_subtype_base,
subtype_rel_self,
is-exception_wf,
equal_wf,
sqle_wf_base,
bfalse_wf,
has-value_wf-partial,
top_wf,
termination,
partial-not-exception,
exception-not-value,
value-type-has-value
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
extract_by_obid,
isectElimination,
thin,
Error :isect_memberEquality_alt,
hypothesisEquality,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
independent_isectElimination,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
callbyvalueDecide,
Error :lambdaFormation_alt,
unionElimination,
lambdaFormation,
unionEquality,
decideExceptionCases,
imageElimination,
imageMemberEquality,
voidElimination,
Error :equalityIsType1
Latex:
\mforall{}[a:partial(Base)]. \mforall{}[b:partial(\mBbbB{})]. (a \mwedge{}\msubb{} b \mmember{} partial(\mBbbB{}))
Date html generated:
2019_06_20-PM-00_34_27
Last ObjectModification:
2018_10_19-PM-00_30_53
Theory : partial_1
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