Nuprl Lemma : sub-bag-empty
∀[T:Type]. ∀[b:bag(T)]. uiff(sub-bag(T;b;{});b = {} ∈ bag(T))
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
empty-bag: {},
bag: bag(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
sub-bag_wf,
empty-bag_wf,
equal-wf-T-base,
bag_wf,
sub-bag-equal,
empty-sub-bag,
sub-bag_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
axiomEquality,
rename,
baseClosed,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
equalityTransitivity,
sqequalRule,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. uiff(sub-bag(T;b;\{\});b = \{\})
Date html generated:
2016_10_25-AM-10_26_46
Last ObjectModification:
2016_07_12-AM-06_42_53
Theory : bags
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