Nuprl Lemma : exp-assoced-one
∀x:ℤ. ∀n:ℕ+. ((x^n ~ 1) ⇒ (x ~ 1))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
exp: i^n,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
exp: i^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nat: ℕ,
decidable: Dec(P)
Lemmas referenced :
primrec-unroll,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
nat_plus_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
assoced_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
exp_wf2,
nat_plus_wf,
mul-assoced-one,
subtract_wf,
decidable__le,
intformnot_wf,
intformle_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
natural_numberEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
independent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
multiplyEquality,
dependent_set_memberEquality
Latex:
\mforall{}x:\mBbbZ{}. \mforall{}n:\mBbbN{}\msupplus{}. ((x\^{}n \msim{} 1) {}\mRightarrow{} (x \msim{} 1))
Date html generated:
2018_05_21-PM-01_06_04
Last ObjectModification:
2018_05_19-AM-06_38_55
Theory : num_thy_1
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