### 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

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