Nuprl Lemma : alt-wkl!_wf
∀[T:Type]. (WKL!(T) ∈ ℙ)
Proof
Definitions occuring in Statement :
alt-wkl!: WKL!(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
and: P ∧ Q,
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
alt-wkl!: WKL!(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
istype-nat,
altpath_wf,
sq_exists_wf,
alt-one-path_wf,
altunbounded_wf,
alttree_wf,
bool_wf,
int_seg_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
Error :universeIsType,
Error :functionIsType,
because_Cache,
Error :lambdaEquality_alt,
productEquality,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
setEquality,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. (WKL!(T) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_46_30
Last ObjectModification:
2019_06_06-PM-01_53_04
Theory : fan-theorem
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