Nuprl Lemma : bag_all_wf
∀[T:Type]. ∀[f:T ⟶ 𝔹]. ∀[b:bag(T)]. (bag_all(b;f) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bag_all: bag_all(b;f),
bag: bag(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
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(b;f),
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 ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s],
bfalse: ff,
prop: ℙ,
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
bag-accum_wf,
bool_wf,
btrue_wf,
eqtt_to_assert,
equal_wf,
iff_imp_equal_bool,
band_wf,
assert_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
iff_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
applyEquality,
functionExtensionality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
productEquality,
addLevel,
impliesFunctionality,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[b:bag(T)]. (bag\_all(b;f) \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-08_52_18
Last ObjectModification:
2017_07_26-PM-04_33_55
Theory : bags
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