Nuprl Lemma : power-set-lift_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (power-set-lift(T;R) ∈ P(T) ⟶ P(T) ⟶ ℙ)
Proof
Definitions occuring in Statement :
power-set-lift: power-set-lift(T;R),
power-set: P(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
power-set-lift: power-set-lift(T;R),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
set-member_wf,
exists_wf,
and_wf,
power-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
functionEquality,
hypothesis,
applyEquality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (power-set-lift(T;R) \mmember{} P(T) {}\mrightarrow{} P(T) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_51_40
Last ObjectModification:
2015_12_26-AM-10_17_09
Theory : bar-induction
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