Nuprl Lemma : divides_invar_1
∀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,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_term_value_minus_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermMinus_wf,
itermMultiply_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
equal_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality,
hypothesisEquality,
multiplyEquality,
hypothesis,
minusEquality,
productElimination,
dependent_pairFormation,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}a,b:\mBbbZ{}. (a | b \mLeftarrow{}{}\mRightarrow{} (-a) | b)
Date html generated:
2016_05_14-PM-04_15_51
Last ObjectModification:
2016_01_14-PM-11_42_40
Theory : num_thy_1
Home
Index