### Nuprl Lemma : natrec_wf

[T:ℕ ⟶ Type]. ∀[g:n:ℕ ⟶ (m:ℕn ⟶ T[m]) ⟶ T[n]].  (letrec f(n)=g[n;f] in f ∈ n:ℕ ⟶ T[n])

Proof

Definitions occuring in Statement :  natrec: natrec int_seg: {i..j-} nat: uall: [x:A]. B[x] so_apply: x[s1;s2] so_apply: x[s] member: t ∈ T function: x:A ⟶ B[x] natural_number: \$n universe: Type
Definitions unfolded in proof :  natrec: natrec uall: [x:A]. B[x] member: t ∈ T nat: so_apply: x[s] subtype_rel: A ⊆B uimplies: supposing a le: A ≤ B and: P ∧ Q less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: all: x:A. B[x] ge: i ≥  guard: {T} genrec: genrec so_apply: x[s1;s2] int_seg: {i..j-} lelt: i ≤ j < k decidable: Dec(P) or: P ∨ Q iff: ⇐⇒ Q rev_implies:  Q uiff: uiff(P;Q) subtract: m top: Top true: True so_lambda: λ2x.t[x] sq_stable: SqStable(P) squash: T
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut sqequalHypSubstitution hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality lemma_by_obid isectElimination thin natural_numberEquality setElimination rename hypothesisEquality applyEquality independent_isectElimination independent_pairFormation lambdaFormation isect_memberEquality because_Cache cumulativity universeEquality intWeakElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination productElimination unionElimination addEquality voidEquality intEquality minusEquality imageMemberEquality baseClosed imageElimination

Latex:
\mforall{}[T:\mBbbN{}  {}\mrightarrow{}  Type].  \mforall{}[g:n:\mBbbN{}  {}\mrightarrow{}  (m:\mBbbN{}n  {}\mrightarrow{}  T[m])  {}\mrightarrow{}  T[n]].    (letrec  f(n)=g[n;f]  in  f  \mmember{}  n:\mBbbN{}  {}\mrightarrow{}  T[n])

Date html generated: 2016_05_13-PM-04_03_11
Last ObjectModification: 2016_01_14-PM-07_24_29

Theory : int_1

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