Nuprl Lemma : fib_coprime
∀n:ℕ. CoPrime(fib(n),fib(n + 1))
Proof
Definitions occuring in Statement :
fib: fib(n),
coprime: CoPrime(a,b),
nat: ℕ,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
ge: i ≥ j ,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
top: Top,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
bfalse: ff,
bor: p ∨bq,
btrue: tt,
ifthenelse: if b then t else f fi ,
subtract: n - m,
eq_int: (i =z j),
fib: fib(n),
coprime: CoPrime(a,b),
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
bnot: ¬bb,
assert: ↑b,
band: p ∧b q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅
Lemmas referenced :
int_term_value_add_lemma,
itermAdd_wf,
nat_properties,
primrec-wf2,
less_than_wf,
set_wf,
nat_wf,
subtract-add-cancel,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__le,
fib_wf,
coprime_wf,
testxxx_lemma,
gcd_p_one,
istype-void,
add-associates,
add-commutes,
add-swap,
zero-add,
bor_wf,
eq_int_wf,
equal-wf-base,
bool_wf,
int_subtype_base,
assert_wf,
istype-assert,
full-omega-unsat,
intformor_wf,
intformeq_wf,
istype-int,
int_formula_prop_or_lemma,
int_formula_prop_eq_lemma,
bnot_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
band_wf,
btrue_wf,
bool_cases_sqequal,
eqff_to_assert,
assert-bnot,
neg_assert_of_eq_int,
bfalse_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert_of_eq_int,
istype-le,
gcd_p_sym,
one-mul,
assert_of_bor,
bnot_thru_bor,
assert_of_band,
gcd_p_shift
Rules used in proof :
addEquality,
applyEquality,
computeAll,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
unionElimination,
hypothesis,
hypothesisEquality,
natural_numberEquality,
dependent_functionElimination,
because_Cache,
dependent_set_memberEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
setElimination,
rename,
thin,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
Error :isect_memberEquality_alt,
baseApply,
closedConclusion,
baseClosed,
unionEquality,
equalityTransitivity,
equalitySymmetry,
Error :equalityIstype,
Error :inhabitedIsType,
sqequalBase,
Error :unionIsType,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
Error :universeIsType,
instantiate,
cumulativity,
productElimination,
promote_hyp,
productEquality,
Error :lambdaFormation_alt,
Error :functionIsType,
Error :productIsType,
Error :dependent_set_memberEquality_alt,
minusEquality,
equalityElimination,
Error :inlFormation_alt,
Error :inrFormation_alt
Latex:
\mforall{}n:\mBbbN{}. CoPrime(fib(n),fib(n + 1))
Date html generated:
2019_06_20-PM-02_25_15
Last ObjectModification:
2019_02_05-PM-03_57_52
Theory : num_thy_1
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