Nuprl Lemma : coprime-exp1
∀a,b:ℤ.  (CoPrime(a,b) 
⇒ (∀n:ℕ. CoPrime(a,b^n)))
Proof
Definitions occuring in Statement : 
coprime: CoPrime(a,b)
, 
exp: i^n
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
int: ℤ
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
top: Top
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
nat: ℕ
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
exp: i^n
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
nequal: a ≠ b ∈ T 
Lemmas referenced : 
coprime_prod, 
neg_assert_of_eq_int, 
assert-bnot, 
bool_subtype_base, 
subtype_base_sq, 
bool_cases_sqequal, 
eqff_to_assert, 
assert_of_eq_int, 
eqtt_to_assert, 
bool_wf, 
eq_int_wf, 
primrec-unroll, 
exists_wf, 
equal_wf, 
int_term_value_mul_lemma, 
int_term_value_add_lemma, 
int_formula_prop_eq_lemma, 
itermMultiply_wf, 
itermAdd_wf, 
intformeq_wf, 
decidable__equal_int, 
coprime_bezout_id, 
nat_wf, 
primrec-wf2, 
less_than_wf, 
set_wf, 
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, 
exp_wf2, 
coprime_wf, 
exp0_lemma
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
thin, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
rename, 
setElimination, 
isectElimination, 
hypothesisEquality, 
dependent_set_memberEquality, 
because_Cache, 
natural_numberEquality, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
independent_pairFormation, 
computeAll, 
introduction, 
productElimination, 
independent_functionElimination, 
addEquality, 
multiplyEquality, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
promote_hyp, 
instantiate, 
cumulativity, 
equalityEquality
Latex:
\mforall{}a,b:\mBbbZ{}.    (CoPrime(a,b)  {}\mRightarrow{}  (\mforall{}n:\mBbbN{}.  CoPrime(a,b\^{}n)))
Date html generated:
2016_05_15-PM-04_49_34
Last ObjectModification:
2016_01_16-AM-11_26_31
Theory : general
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