Nuprl Lemma : bag-product-primes
∀b:bag(Prime). 0 < Π(b)
Proof
Definitions occuring in Statement :
Prime: Prime,
int-bag-product: Π(b),
bag: bag(T),
less_than: a < b,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
Prime: Prime,
int_upper: {i...},
implies: P ⇒ Q,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
l_member: (x ∈ l),
cand: A c∧ B,
sq_type: SQType(T),
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top
Lemmas referenced :
bag_wf,
Prime_wf,
int-bag-product-positive,
subtype_rel_bag,
bag_to_squash_list,
bag-member_wf,
bag-member-list,
decidable__int_equal,
subtype_rel_list,
subtype_base_sq,
int_subtype_base,
select_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
int_upper_properties,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
equal_wf,
member-less_than
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
intEquality,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
because_Cache,
sqequalRule,
isect_memberFormation,
imageElimination,
productElimination,
promote_hyp,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
independent_functionElimination,
dependent_functionElimination,
instantiate,
cumulativity,
equalityTransitivity,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}b:bag(Prime). 0 < \mPi{}(b)
Date html generated:
2018_05_21-PM-07_22_45
Last ObjectModification:
2017_07_26-PM-05_05_52
Theory : general
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