Nuprl Lemma : wkl!-iff-twkl!-bool
WKL! ⇐⇒ WKL!(𝔹)
Proof
Definitions occuring in Statement :
wkl!: WKL!,
twkl!: WKL!(T),
bool: 𝔹,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
twkl!: WKL!(T),
wkl!: WKL!,
down-closed: down-closed(T;X),
eff-unique: eff-unique(A),
infinite-tree: infinite-tree(A),
R-closed: R-closed(T;x.X[x];a,b.R[a; b]),
eff-unique-path: eff-unique-path(T;A),
dec-predicate: Decidable(X),
unbounded-list-predicate: Unbounded(A),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
cand: A c∧ B,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
list_wf,
bool_wf,
and_wf,
all_wf,
iseg_wf,
unbounded-list-predicate_wf,
eff-unique-path_wf,
dec-predicate_wf,
set_wf,
sq_exists_wf,
nat_wf,
is-path_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
independent_pairFormation,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
lemma_by_obid,
isectElimination,
functionEquality,
cumulativity,
universeEquality,
because_Cache,
lambdaEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
productElimination,
independent_functionElimination,
productEquality
Latex:
WKL! \mLeftarrow{}{}\mRightarrow{} WKL!(\mBbbB{})
Date html generated:
2016_05_14-PM-04_12_47
Last ObjectModification:
2015_12_26-PM-07_54_14
Theory : fan-theorem
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