Nuprl Lemma : decidable__upwd-closure
∀[T:Type]. ∀[A:(T List) ⟶ ℙ]. (Decidable(A) ⇒ (∀as:T List. Dec(upwd-closure(T;A) as)))
Proof
Definitions occuring in Statement :
upwd-closure: upwd-closure(T;A),
dec-predicate: Decidable(X),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
upwd-closure: upwd-closure(T;A),
dec-predicate: Decidable(X),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
decidable__exists_iseg,
list_wf,
all_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[A:(T List) {}\mrightarrow{} \mBbbP{}]. (Decidable(A) {}\mRightarrow{} (\mforall{}as:T List. Dec(upwd-closure(T;A) as)))
Date html generated:
2016_05_14-PM-04_10_03
Last ObjectModification:
2015_12_26-PM-07_54_25
Theory : fan-theorem
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