Nuprl Lemma : bag-lub_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs,as:bag(T)]. (bag-lub(eq;bs;as) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-lub: bag-lub(eq;b1;b2),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-lub: bag-lub(eq;b1;b2),
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
bag-combine_wf,
bag-to-set_wf,
bag-append_wf,
bag-rep_wf,
imax_wf,
bag-count_wf,
imax_nat,
nat_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_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_eq_lemma,
int_formula_prop_wf,
equal_wf,
le_wf,
list-subtype-bag,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
dependent_set_memberEquality,
applyEquality,
setElimination,
rename,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs,as:bag(T)]. (bag-lub(eq;bs;as) \mmember{} bag(T))
Date html generated:
2018_05_21-PM-09_52_16
Last ObjectModification:
2017_07_26-PM-06_31_46
Theory : bags_2
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