Nuprl Lemma : gcd_exists
∀a,b:ℤ. ∃y:ℤ. GCD(a;b;y)
Proof
Definitions occuring in Statement :
gcd_p: GCD(a;b;y),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
exists: ∃x:A. B[x],
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top
Lemmas referenced :
decidable__le,
istype-int,
gcd_exists_n,
le_wf,
gcd_p_neg_arg_2,
gcd_p_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMinus_wf,
itermVar_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_minus_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
unionElimination,
Error :inhabitedIsType,
Error :dependent_set_memberEquality_alt,
Error :universeIsType,
isectElimination,
productElimination,
Error :dependent_pairFormation_alt,
independent_functionElimination,
because_Cache,
minusEquality,
independent_isectElimination,
approximateComputation,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation
Latex:
\mforall{}a,b:\mBbbZ{}. \mexists{}y:\mBbbZ{}. GCD(a;b;y)
Date html generated:
2019_06_20-PM-02_22_17
Last ObjectModification:
2018_10_03-AM-00_12_24
Theory : num_thy_1
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