Nuprl Lemma : bag-deq-member-bag-diff
∀[T:Type]. ∀eq:EqDecider(T). ∀x:T. ∀bs:bag(T). (bag-deq-member(eq;x;bs) ~ isl(bag-diff(eq;bs;{x})))
Proof
Definitions occuring in Statement :
bag-diff: bag-diff(eq;bs;as),
bag-deq-member: bag-deq-member(eq;x;b),
single-bag: {x},
bag: bag(T),
deq: EqDecider(T),
isl: isl(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
bag-member-bag-diff,
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
bag-deq-member_wf,
isl_wf,
bag_wf,
unit_wf2,
bag-diff_wf,
single-bag_wf,
bag-member_wf,
assert_wf,
assert-bag-deq-member,
iff_wf,
deq_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
productElimination,
instantiate,
because_Cache,
independent_isectElimination,
independent_pairFormation,
addLevel,
impliesFunctionality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}x:T. \mforall{}bs:bag(T). (bag-deq-member(eq;x;bs) \msim{} isl(bag-diff(eq;bs;\{x\})))
Date html generated:
2016_05_15-PM-08_05_22
Last ObjectModification:
2015_12_27-PM-04_14_08
Theory : bags_2
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