### Nuprl Lemma : bar-val_wf

`∀[n:ℕ]. ∀[T:Type]. ∀[x:bar-base(T)].  (bar-val(n;x) ∈ T?)`

Proof

Definitions occuring in Statement :  bar-val: `bar-val(n;x)` bar-base: `bar-base(T)` nat: `ℕ` uall: `∀[x:A]. B[x]` unit: `Unit` member: `t ∈ T` union: `left + right` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` bar-val: `bar-val(n;x)` subtype_rel: `A ⊆r B` all: `∀x:A. B[x]` eq_int: `(i =z j)` subtract: `n - m` ifthenelse: `if b then t else f fi ` btrue: `tt` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` uiff: `uiff(P;Q)` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` exposed-bfalse: `exposed-bfalse` bool: `𝔹` unit: `Unit` it: `⋅` bfalse: `ff` exists: `∃x:A. B[x]` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality applyEquality unionEquality unionElimination inlEquality inrEquality because_Cache independent_pairFormation productElimination addEquality voidEquality intEquality minusEquality equalityElimination dependent_pairFormation promote_hyp instantiate

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[T:Type].  \mforall{}[x:bar-base(T)].    (bar-val(n;x)  \mmember{}  T?)

Date html generated: 2017_04_14-AM-07_45_55
Last ObjectModification: 2017_02_27-PM-03_16_32

Theory : co-recursion

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