Nuprl Lemma : sub-bag-cancel-right
∀[T:Type]. ∀b1,b2,b:bag(T). (sub-bag(T;b1 + b;b2 + b) ⇐⇒ sub-bag(T;b1;b2))
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
bag-append: as + bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sub-bag: sub-bag(T;as;bs),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
top: Top,
uiff: uiff(P;Q),
uimplies: b supposing a,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
equal_wf,
bag_wf,
bag-append_wf,
exists_wf,
bag-append-comm,
bag-append-assoc,
bag-append-cancel,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesis,
sqequalRule,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
hyp_replacement,
applyLambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
applyEquality,
imageElimination,
equalityUniverse,
levelHypothesis,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}b1,b2,b:bag(T). (sub-bag(T;b1 + b;b2 + b) \mLeftarrow{}{}\mRightarrow{} sub-bag(T;b1;b2))
Date html generated:
2017_10_01-AM-08_53_04
Last ObjectModification:
2017_07_26-PM-04_34_37
Theory : bags
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