Nuprl Lemma : sub-bag-append-left2
∀[T:Type]. ∀b1,b2,b:bag(T). (sub-bag(T;b1 + b2;b) ⇒ sub-bag(T;b2;b))
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],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
sub-bag: sub-bag(T;as;bs),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
sub-bag_wf,
squash_wf,
true_wf,
bag-append-comm,
iff_weakening_equal,
bag-append_wf,
bag-append-assoc,
equal_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_pairFormation,
cumulativity,
isect_memberEquality,
voidElimination,
voidEquality,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}b1,b2,b:bag(T). (sub-bag(T;b1 + b2;b) {}\mRightarrow{} sub-bag(T;b2;b))
Date html generated:
2016_10_25-AM-10_26_35
Last ObjectModification:
2016_07_12-AM-06_42_37
Theory : bags
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