Nuprl Lemma : sub-bag_transitivity
∀[T:Type]. ∀[as,bs,cs:bag(T)]. (sub-bag(T;as;bs) ⇒ sub-bag(T;bs;cs) ⇒ sub-bag(T;as;cs))
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
sub-bag: sub-bag(T;as;bs),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
top: Top,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
bag-append_wf,
bag-append-assoc2,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
bag_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
rename,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs,cs:bag(T)]. (sub-bag(T;as;bs) {}\mRightarrow{} sub-bag(T;bs;cs) {}\mRightarrow{} sub-bag(T;as;cs))
Date html generated:
2017_10_01-AM-08_52_55
Last ObjectModification:
2017_07_26-PM-04_34_20
Theory : bags
Home
Index