Nuprl Lemma : bag-lub-comm
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:bag(T)]. (bag-lub(eq;as;bs) = 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],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-lub: bag-lub(eq;b1;b2),
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nat: ℕ,
label: ...$L... t,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
ge: i ≥ j ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
bag-to-set_wf,
bag-append-comm,
bag-append_wf,
iff_weakening_equal,
bag-rep_wf,
nat_wf,
imax_com,
bag-count_wf,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
imax_nat,
nat_properties,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
le_wf,
list-subtype-bag,
imax_wf,
bag-combine_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
because_Cache,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
cumulativity,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
lambdaFormation,
applyLambdaEquality,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:bag(T)]. (bag-lub(eq;as;bs) = bag-lub(eq;bs;as))
Date html generated:
2018_05_21-PM-09_52_19
Last ObjectModification:
2017_07_26-PM-06_31_48
Theory : bags_2
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