Nuprl Lemma : bag-parts'_wf
∀[T:Type]
∀[eq:EqDecider(T)]. ∀[x:T]. ∀[bs:bag(T)]. (bag-parts'(eq;bs;x) ∈ bag(bag(T) List+)) supposing valueall-type(T)
Proof
Definitions occuring in Statement :
bag-parts': bag-parts'(eq;bs;x),
bag: bag(T),
listp: A List+,
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag-parts': bag-parts'(eq;bs;x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
listp: A List+,
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
bag-null_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bag_wf,
eqtt_to_assert,
assert-bag-null,
single-bag_wf,
listp_wf,
cons_wf_listp,
nil_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
valueall-type-has-valueall,
bag-valueall-type,
set-valueall-type,
list_wf,
less_than_wf,
length_wf,
list-valueall-type,
bag-parts_wf,
evalall-reduce,
bag-append_wf,
bag-map_wf,
empty-bag_wf,
bag-filter_wf,
eq_int_wf,
bag-count_wf,
hd_wf,
listp_properties,
nat_wf,
subtype_rel_bag,
equal_wf,
deq_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
isectElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
independent_pairFormation,
impliesFunctionality,
lambdaEquality,
natural_numberEquality,
callbyvalueReduce,
setElimination,
rename,
applyEquality,
setEquality,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[bs:bag(T)]. (bag-parts'(eq;bs;x) \mmember{} bag(bag(T) List\msupplus{}))
supposing valueall-type(T)
Date html generated:
2018_05_21-PM-09_51_10
Last ObjectModification:
2017_07_26-PM-06_31_28
Theory : bags_2
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