Nuprl Lemma : fib_wf
∀[n:ℕ]. (fib(n) ∈ ℕ)
Proof
Definitions occuring in Statement :
fib: fib(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
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,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
fib: fib(n),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
le_wf,
decidable__lt,
lelt_wf,
itermAdd_wf,
int_term_value_add_lemma,
nat_wf,
bor_wf,
eq_int_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
or_wf,
band_wf,
bnot_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
assert_of_bor,
assert_of_eq_int,
bnot_thru_bor,
eqff_to_assert,
assert_of_band,
assert_of_bnot,
equal_wf,
add_nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
productElimination,
unionElimination,
applyEquality,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
addEquality,
baseClosed,
productEquality,
equalityElimination,
orFunctionality,
impliesFunctionality
Latex:
\mforall{}[n:\mBbbN{}]. (fib(n) \mmember{} \mBbbN{})
Date html generated:
2017_04_17-AM-09_43_55
Last ObjectModification:
2017_02_27-PM-05_38_38
Theory : num_thy_1
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