Nuprl Lemma : empty-sub-bag
∀T:Type. ∀b:bag(T). sub-bag(T;{};b)
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
empty-bag: {},
bag: bag(T),
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
sub-bag: sub-bag(T;as;bs),
exists: ∃x:A. B[x],
member: t ∈ T,
top: Top,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
empty_bag_append_lemma,
equal_wf,
bag_wf,
bag-append_wf,
empty-bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
hypothesisEquality,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}b:bag(T). sub-bag(T;\{\};b)
Date html generated:
2016_05_15-PM-02_36_17
Last ObjectModification:
2015_12_27-AM-09_44_53
Theory : bags
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