### Nuprl Lemma : primtailrec-unroll

`∀[n:ℤ]. ∀[b,c:Top].  (primtailrec(n;0;b;c) ~ if n <z 1 then b else c (n - 1) primtailrec(n - 1;0;b;c) fi )`

Proof

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

Latex:
\mforall{}[n:\mBbbZ{}].  \mforall{}[b,c:Top].
(primtailrec(n;0;b;c)  \msim{}  if  n  <z  1  then  b  else  c  (n  -  1)  primtailrec(n  -  1;0;b;c)  fi  )

Date html generated: 2019_06_20-AM-11_27_28
Last ObjectModification: 2019_01_28-PM-05_02_19

Theory : call!by!value_2

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