Nuprl Lemma : divides_invar_2
∀a,b:ℤ. (a | b ⇐⇒ a | (-b))
Proof
Definitions occuring in Statement :
divides: b | a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
minus: -n,
int: ℤ
Definitions unfolded in proof :
divides: b | a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
squash: ↓T,
true: True,
guard: {T}
Lemmas referenced :
int_subtype_base,
istype-int,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermMinus_wf,
itermVar_wf,
itermMultiply_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_minus_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_wf,
equal_wf,
squash_wf,
true_wf,
minus_minus_cancel,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
independent_pairFormation,
Error :productIsType,
Error :inhabitedIsType,
hypothesisEquality,
Error :equalityIsType4,
cut,
applyEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
multiplyEquality,
minusEquality,
because_Cache,
productElimination,
thin,
Error :dependent_pairFormation_alt,
dependent_functionElimination,
unionElimination,
isectElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
imageMemberEquality,
baseClosed,
instantiate
Latex:
\mforall{}a,b:\mBbbZ{}. (a | b \mLeftarrow{}{}\mRightarrow{} a | (-b))
Date html generated:
2019_06_20-PM-02_19_57
Last ObjectModification:
2018_10_03-AM-00_35_39
Theory : num_thy_1
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