### Nuprl Lemma : nth-fibs

`∀n:ℕ. (s-nth(n;fibs()) = fib(n) ∈ ℤ)`

Proof

Definitions occuring in Statement :  fibs: `fibs()` fib: `fib(n)` s-nth: `s-nth(n;s)` nat: `ℕ` all: `∀x:A. B[x]` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` fibs: `fibs()` fib: `fib(n)` s-nth: `s-nth(n;s)` s-cons: `x.s` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` bnot: `¬bb` assert: `↑b` bor: `p ∨bq` le: `A ≤ B` less_than': `less_than'(a;b)` int_upper: `{i...}` has-value: `(a)↓` nequal: `a ≠ b ∈ T ` squash: `↓T` true: `True` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtract: `n - m`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation axiomEquality because_Cache productElimination unionElimination applyEquality instantiate equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality hypothesis_subsumption equalityElimination promote_hyp cumulativity callbyvalueReduce addEquality imageElimination universeEquality imageMemberEquality baseClosed minusEquality

Latex:
\mforall{}n:\mBbbN{}.  (s-nth(n;fibs())  =  fib(n))

Date html generated: 2018_05_21-PM-00_59_57
Last ObjectModification: 2018_05_19-AM-06_36_41

Theory : num_thy_1

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