Nuprl Lemma : sub-bag_weakening
∀[T:Type]. ∀[as,bs:bag(T)]. ((as = bs ∈ bag(T)) ⇒ sub-bag(T;as;bs))
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,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
sub-bag: sub-bag(T;as;bs),
exists: ∃x:A. B[x],
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,
rev_implies: P ⇐ Q
Lemmas referenced :
empty-bag_wf,
equal_wf,
squash_wf,
true_wf,
bag-append_wf,
iff_weakening_equal,
bag-append-ident,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
equalitySymmetry,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
because_Cache,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:bag(T)]. ((as = bs) {}\mRightarrow{} sub-bag(T;as;bs))
Date html generated:
2017_10_01-AM-08_52_50
Last ObjectModification:
2017_07_26-PM-04_34_17
Theory : bags
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