Nuprl Lemma : bag-single-no-repeats
∀[T:Type]. ∀[x:T]. bag-no-repeats(T;{x})
Proof
Definitions occuring in Statement :
bag-no-repeats: bag-no-repeats(T;bs),
single-bag: {x},
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
single-bag: {x},
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,
prop: ℙ,
squash: ↓T
Lemmas referenced :
cons_wf,
nil_wf,
list-subtype-bag,
no_repeats_singleton,
equal_wf,
bag_wf,
no_repeats_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
independent_isectElimination,
lambdaEquality,
sqequalRule,
independent_pairFormation,
productEquality,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. bag-no-repeats(T;\{x\})
Date html generated:
2017_10_01-AM-08_51_46
Last ObjectModification:
2017_07_26-PM-04_33_32
Theory : bags
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