Nuprl Lemma : empty-bag-no-repeats
∀[T:Type]. bag-no-repeats(T;{})
Proof
Definitions occuring in Statement :
bag-no-repeats: bag-no-repeats(T;bs),
empty-bag: {},
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
empty-bag: {},
bag-no-repeats: bag-no-repeats(T;bs),
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
prop: ℙ,
squash: ↓T
Lemmas referenced :
no_repeats_wf,
bag_wf,
equal-wf-T-base,
no_repeats_nil,
list-subtype-bag,
nil_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
voidEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
voidElimination,
sqequalRule,
independent_pairFormation,
isect_memberEquality,
productEquality,
because_Cache,
baseClosed,
cumulativity,
imageMemberEquality,
imageElimination,
universeEquality
Latex:
\mforall{}[T:Type]. bag-no-repeats(T;\{\})
Date html generated:
2016_05_15-PM-02_33_46
Last ObjectModification:
2016_01_16-AM-08_52_16
Theory : bags
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