Nuprl Lemma : twkl!_wf
∀[T:Type]. (WKL!(T) ∈ ℙ')
Proof
Definitions occuring in Statement :
twkl!: WKL!(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
twkl!: WKL!(T),
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
list_wf,
down-closed_wf,
unbounded-list-predicate_wf,
and_wf,
dec-predicate_wf,
eff-unique-path_wf,
sq_exists_wf,
nat_wf,
is-path_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
setEquality,
functionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
universeEquality,
productEquality,
because_Cache,
lambdaFormation,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. (WKL!(T) \mmember{} \mBbbP{}')
Date html generated:
2016_05_14-PM-04_10_30
Last ObjectModification:
2015_12_26-PM-07_54_15
Theory : fan-theorem
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