Nuprl Lemma : per-union_wf
∀[A,B:Type]. (per-union(A;B) ∈ Type)
Proof
Definitions occuring in Statement :
per-union: per-union(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
uimplies: b supposing a,
uand: uand(A;B),
has-value: (a)↓,
top: Top,
per-union: per-union(A;B),
outl: outl(x),
outr: outr(x),
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
uand_wf,
has-value_wf_base,
is-exception_wf,
istype-top,
istype-void,
equal-wf-base,
per-void_wf,
sqle_wf_base,
istype-universe,
if-per-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
hypothesisEquality,
Error :isect_memberEquality_alt,
isectElimination,
thin,
Error :universeIsType,
universeEquality,
extract_by_obid,
isectEquality,
because_Cache,
baseClosed,
axiomSqleEquality,
divergentSqle,
sqleReflexivity,
rename,
isaxiomCases,
independent_isectElimination,
promote_hyp,
axiomSqEquality,
voidElimination,
pertypeEquality,
isinlCases,
baseApply,
closedConclusion,
isinrCases,
Error :lambdaFormation_alt,
Error :isectIsType,
Error :equalityIsType4,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. (per-union(A;B) \mmember{} Type)
Date html generated:
2019_06_20-AM-11_30_41
Last ObjectModification:
2018_10_07-PM-08_29_40
Theory : per!type
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