### Nuprl Lemma : primrec_wf

`∀[T:Type]. ∀[n:ℕ]. ∀[b:T]. ∀[c:ℕn ⟶ T ⟶ T].  (primrec(n;b;c) ∈ T)`

Proof

Definitions occuring in Statement :  primrec: `primrec(n;b;c)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` and: `P ∧ Q` ge: `i ≥ j ` le: `A ≤ B` cand: `A c∧ B` less_than: `a < b` squash: `↓T` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` top: `Top` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` subtract: `n - m` less_than': `less_than'(a;b)` true: `True` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination Error :lambdaFormation_alt,  independent_pairFormation productElimination imageElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination Error :universeIsType,  Error :lambdaEquality_alt,  dependent_functionElimination Error :isect_memberEquality_alt,  axiomEquality equalityTransitivity equalitySymmetry Error :isectIsTypeImplies,  Error :inhabitedIsType,  Error :functionIsTypeImplies,  unionElimination equalityElimination because_Cache Error :dependent_pairFormation_alt,  Error :equalityIstype,  promote_hyp instantiate cumulativity Error :functionIsType,  applyEquality Error :dependent_set_memberEquality_alt,  addEquality minusEquality Error :productIsType,  functionEquality intEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[b:T].  \mforall{}[c:\mBbbN{}n  {}\mrightarrow{}  T  {}\mrightarrow{}  T].    (primrec(n;b;c)  \mmember{}  T)

Date html generated: 2019_06_20-AM-11_27_41
Last ObjectModification: 2019_01_28-PM-05_28_01

Theory : call!by!value_2

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