Nuprl Lemma : only_pm_one_divs_one
∀b:ℤ. ((b | 1) ⇒ b = ± 1)
Proof
Definitions occuring in Statement :
divides: b | a,
pm_equal: i = ± j,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
prop: ℙ,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
uimplies: b supposing a,
decidable: Dec(P),
or: P ∨ Q,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
pm_equal: i = ± j,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
divides_wf,
nat_wf,
istype-int,
divisors_bound,
less_than_wf,
decidable__equal_int,
zero_divs_only_zero,
nat_properties,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
decidable__le,
int_subtype_base,
le_wf,
itermMinus_wf,
int_term_value_minus_lemma,
divides_invar_1,
minus-minus
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
hypothesis,
Error :universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
Error :dependent_set_memberEquality_alt,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
baseClosed,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
equalityTransitivity,
because_Cache,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :inlFormation_alt,
Error :equalityIsType4,
Error :inhabitedIsType,
applyEquality,
minusEquality,
productElimination,
Error :inrFormation_alt
Latex:
\mforall{}b:\mBbbZ{}. ((b | 1) {}\mRightarrow{} b = \mpm{} 1)
Date html generated:
2019_06_20-PM-02_20_00
Last ObjectModification:
2018_10_03-AM-00_35_40
Theory : num_thy_1
Home
Index