Nuprl Lemma : strong-type-continuous_wf
∀[F:Type ⟶ Type]. (Continuous+(t.F[t]) ∈ ℙ')
Proof
Definitions occuring in Statement : 
strong-type-continuous: Continuous+(T.F[T])
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
strong-type-continuous: Continuous+(T.F[T])
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
so_apply: x[s]
Lemmas referenced : 
uall_wf, 
nat_wf, 
ext-eq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
thin, 
instantiate, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
functionEquality, 
cumulativity, 
hypothesis, 
universeEquality, 
lambdaEquality, 
isectEquality, 
applyEquality, 
hypothesisEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[F:Type  {}\mrightarrow{}  Type].  (Continuous+(t.F[t])  \mmember{}  \mBbbP{}')
Date html generated:
2016_05_13-PM-04_09_36
Last ObjectModification:
2015_12_26-AM-11_22_41
Theory : subtype_1
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