Nuprl Lemma : nwkl!-iff-twkl!-bool
nWKL! ⇐⇒ WKL!(𝔹)
Proof
Definitions occuring in Statement :
nwkl!: nWKL!,
twkl!: WKL!(T),
bool: 𝔹,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
twkl!: WKL!(T),
nwkl!: nWKL!,
eff-unique: eff-unique(A),
eff-unique-path: eff-unique-path(T;A),
dec-predicate: Decidable(X),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
sq_exists: ∃x:{A| B[x]},
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
squash: ↓T,
infinite-tree: infinite-tree(A),
nat: ℕ,
down-closed: down-closed(T;X),
R-closed: R-closed(T;x.X[x];a,b.R[a; b]),
guard: {T},
unbounded-list-predicate: Unbounded(A),
cand: A c∧ B,
is-path: is-path(A;f),
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
is-path_wf,
bool_wf,
nat_wf,
eff-unique-path_wf,
dec-predicate_wf,
list_wf,
set_wf,
down-closed_wf,
unbounded-list-predicate_wf,
all_wf,
infinite-tree_wf,
exists_wf,
sq_exists_wf,
sq_stable__and,
iseg_wf,
equal_wf,
length_wf,
sq_stable__all,
sq_stable_from_decidable,
decidable__exists_length_bool,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
upto_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
independent_pairFormation,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
independent_functionElimination,
productElimination,
dependent_set_memberFormation,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
functionExtensionality,
applyEquality,
instantiate,
functionEquality,
cumulativity,
universeEquality,
lambdaEquality,
productEquality,
dependent_pairFormation,
setEquality,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
intEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_isectElimination
Latex:
nWKL! \mLeftarrow{}{}\mRightarrow{} WKL!(\mBbbB{})
Date html generated:
2017_04_17-AM-09_39_08
Last ObjectModification:
2017_02_27-PM-05_35_17
Theory : fan-theorem
Home
Index