### Nuprl Lemma : primrec-unroll-1

`∀[n:{n:ℤ| 0 < n} ]. ∀[b,c:Top].  (primrec(n;b;c) ~ c (n - 1) primrec(n - 1;b;c))`

Proof

Definitions occuring in Statement :  primrec: `primrec(n;b;c)` less_than: `a < b` uall: `∀[x:A]. B[x]` top: `Top` set: `{x:A| B[x]} ` 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 ` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` not: `¬A` less_than': `less_than'(a;b)` true: `True` false: `False` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  primrec-unroll lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int less-iff-le add_functionality_wrt_le add-associates add-zero add-commutes le-add-cancel2 eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base iff_transitivity assert_wf bnot_wf not_wf less_than_wf iff_weakening_uiff assert_of_bnot top_wf set_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis because_Cache natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination dependent_functionElimination addEquality applyEquality lambdaEquality isect_memberEquality voidElimination voidEquality intEquality independent_functionElimination dependent_pairFormation promote_hyp instantiate cumulativity independent_pairFormation impliesFunctionality sqequalAxiom

Latex:
\mforall{}[n:\{n:\mBbbZ{}|  0  <  n\}  ].  \mforall{}[b,c:Top].    (primrec(n;b;c)  \msim{}  c  (n  -  1)  primrec(n  -  1;b;c))

Date html generated: 2018_05_21-PM-00_02_53
Last ObjectModification: 2018_05_19-AM-07_12_41

Theory : call!by!value_2

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