Nuprl Lemma : per-union-implies-wf1
∀[A,B:Type]. ∀[x:per-union(A;B)]. (x ~ inl outl(x) ∈ ℙ)
Proof
Definitions occuring in Statement :
per-union: per-union(A;B),
outl: outl(x),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
inl: inl x,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
per-union: per-union(A;B),
has-value: (a)↓,
outl: outl(x),
uand: uand(A;B),
guard: {T},
top: Top,
outr: outr(x),
sq_type: SQType(T),
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
true: True
Lemmas referenced :
sqequal-wf-base,
member_wf,
subtype_base_sq,
subtype_rel_self,
has-value_wf_base,
is-exception_wf,
cbv-sqequal0,
istype-top,
istype-void,
uand_wf,
equal-wf-base,
per-void_wf,
istype-sqequal,
per-union_wf,
istype-universe,
if-per-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
pointwiseFunctionality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesis,
applyEquality,
instantiate,
Error :lambdaEquality_alt,
imageElimination,
because_Cache,
universeEquality,
sqequalExtensionalEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
independent_isectElimination,
pertypeElimination,
promote_hyp,
axiomSqleEquality,
divergentSqle,
sqleReflexivity,
isinlCases,
axiomSqEquality,
Error :inhabitedIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
voidElimination,
Error :universeIsType,
isectEquality,
isinrCases,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
imageMemberEquality,
natural_numberEquality,
rename,
isaxiomCases
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:per-union(A;B)]. (x \msim{} inl outl(x) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_30_43
Last ObjectModification:
2019_01_03-PM-03_54_29
Theory : per!type
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