`∀[T:Type]. ∀[n,m:ℕ]. ∀[b:T]. ∀[c:ℕn + m ⟶ T ⟶ T].  (primrec(n + m;b;c) ~ primrec(n;primrec(m;b;c);λi,t. (c (i + m) t))\000C)`

Proof

Definitions occuring in Statement :  primrec: `primrec(n;b;c)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` apply: `f a` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` universe: `Type` sqequal: `s ~ t`
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` all: `∀x:A. B[x]` top: `Top` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` uiff: `uiff(P;Q)` subtract: `n - m` subtype_rel: `A ⊆r B` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` so_lambda: `λ2x.t[x]` so_apply: `x[s]` int_seg: `{i..j-}` lelt: `i ≤ j < k` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination independent_functionElimination voidElimination sqequalRule lambdaEquality dependent_functionElimination isect_memberEquality axiomSqEquality functionEquality addEquality because_Cache voidEquality Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  unionElimination independent_pairFormation productElimination applyEquality intEquality minusEquality setEquality equalityElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp instantiate cumulativity universeEquality multiplyEquality dependent_set_memberEquality imageMemberEquality baseClosed

Latex:
\mforall{}[T:Type].  \mforall{}[n,m:\mBbbN{}].  \mforall{}[b:T].  \mforall{}[c:\mBbbN{}n  +  m  {}\mrightarrow{}  T  {}\mrightarrow{}  T].
(primrec(n  +  m;b;c)  \msim{}  primrec(n;primrec(m;b;c);\mlambda{}i,t.  (c  (i  +  m)  t)))

Date html generated: 2019_06_20-AM-11_27_47
Last ObjectModification: 2018_09_26-AM-10_58_09

Theory : call!by!value_2

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