Nuprl Lemma : lcm_wf
∀[a,b:ℤ]. (lcm(a;b) ∈ ℤ)
Proof
Definitions occuring in Statement :
lcm: lcm(a;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lcm: lcm(a;b),
has-value: (a)↓,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
value-type-has-value,
int-value-type,
eq_int_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
gcd_wf,
divide_wfa,
gcd-non-zero,
full-omega-unsat,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformnot_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
int_subtype_base,
nequal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
because_Cache,
closedConclusion,
natural_numberEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
Error :dependent_pairFormation_alt,
Error :equalityIstype,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
multiplyEquality,
Error :dependent_set_memberEquality_alt,
Error :inlFormation_alt,
approximateComputation,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
independent_pairFormation,
Error :universeIsType,
applyEquality,
baseClosed,
sqequalBase,
axiomEquality,
Error :isectIsTypeImplies
Latex:
\mforall{}[a,b:\mBbbZ{}]. (lcm(a;b) \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-PM-02_27_23
Last ObjectModification:
2019_03_06-AM-11_09_28
Theory : num_thy_1
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