Nuprl Lemma : bezout_ident
∀a,b:ℤ. ∃u,v:ℤ. GCD(a;b;(u * a) + (v * b))
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
multiply: n * m,
add: n + m,
int: ℤ
Definitions unfolded in proof :
or: P ∨ Q,
decidable: Dec(P),
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
nat: ℕ,
and: P ∧ Q,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a
Lemmas referenced :
decidable__le,
le_wf,
bezout_ident_n,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_minus_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermMinus_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
gcd_p_neg_arg,
gcd_p_wf,
istype-void,
minus-one-mul,
mul-associates,
mul-commutes,
minus-minus,
mul-swap
Rules used in proof :
intEquality,
unionElimination,
hypothesis,
hypothesisEquality,
natural_numberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
isectElimination,
dependent_set_memberEquality,
productElimination,
computeAll,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
minusEquality,
because_Cache,
Error :dependent_pairFormation_alt,
addEquality,
multiplyEquality,
independent_functionElimination,
Error :universeIsType,
Error :productIsType,
Error :inhabitedIsType,
Error :isect_memberEquality_alt
Latex:
\mforall{}a,b:\mBbbZ{}. \mexists{}u,v:\mBbbZ{}. GCD(a;b;(u * a) + (v * b))
Date html generated:
2019_06_20-PM-02_22_23
Last ObjectModification:
2019_01_13-AM-11_46_17
Theory : num_thy_1
Home
Index