Nuprl Lemma : bag-all_wf
∀[T:Type]. ∀[p:T ⟶ 𝔹]. ∀[bs:bag(T)]. (bag-all(x.p[x];bs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bag-all: bag-all(x.p[x];bs),
bag: bag(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-all: bag-all(x.p[x];bs),
so_lambda: λ2x y.t[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
so_apply: x[s1;s2],
uimplies: b supposing a,
comm: Comm(T;op),
infix_ap: x f y,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
assoc: Assoc(T;op),
top: Top,
uiff: uiff(P;Q),
so_apply: x[s]
Lemmas referenced :
bag-reduce_wf,
bool_wf,
btrue_wf,
equal_wf,
squash_wf,
true_wf,
band_commutes,
iff_weakening_equal,
band_assoc,
eqtt_to_assert,
bag-map_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
independent_isectElimination,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
isect_memberEquality,
axiomEquality,
voidElimination,
voidEquality,
cumulativity,
functionExtensionality,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[p:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[bs:bag(T)]. (bag-all(x.p[x];bs) \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-08_52_13
Last ObjectModification:
2017_07_26-PM-04_33_53
Theory : bags
Home
Index