Nuprl Lemma : nth-better-fibs
∀n:ℕ. (s-nth(n;better-fibs()) = fib(n) ∈ ℤ)
Proof
Definitions occuring in Statement :
better-fibs: better-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],
better-fibs: better-fibs(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
fib: fib(n),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
bor: p ∨bq,
bfalse: ff,
s-nth: s-nth(n;s),
mk-stream: mk-stream(f;x),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
pi1: fst(t),
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a)
Lemmas referenced :
nth-stream-map,
nat_wf,
mk-stream_wf,
value-type-has-value,
int-value-type,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
false_wf,
product-valueall-type,
set-valueall-type,
int-valueall-type,
stream-subtype,
top_wf,
testxxx_lemma,
intformless_wf,
int_formula_prop_less_lemma,
ge_wf,
less_than_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
fib_wf,
squash_wf,
true_wf,
add-zero,
add-commutes,
add-associates,
zero-add,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
minus-one-mul-top,
add-swap,
add_functionality_wrt_le,
le-add-cancel,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
product_subtype_base,
int_subtype_base,
set_subtype_base,
decidable__equal_int,
valueall-type-has-valueall,
evalall-reduce,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
productEquality,
because_Cache,
lambdaEquality,
productElimination,
callbyvalueReduce,
intEquality,
independent_isectElimination,
addEquality,
setElimination,
rename,
independent_pairEquality,
dependent_set_memberEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
applyEquality,
intWeakElimination,
axiomEquality,
equalityElimination,
sqleReflexivity,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
minusEquality,
promote_hyp,
instantiate,
cumulativity,
universeEquality
Latex:
\mforall{}n:\mBbbN{}. (s-nth(n;better-fibs()) = fib(n))
Date html generated:
2017_04_17-AM-09_49_23
Last ObjectModification:
2017_02_27-PM-05_45_45
Theory : num_thy_1
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