Nuprl Lemma : bag-has-no-repeats_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[b:bag(T)]. (bag-has-no-repeats(eq;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bag-has-no-repeats: bag-has-no-repeats(eq;b),
bag: bag(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-has-no-repeats: bag-has-no-repeats(eq;b),
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
eq_int_wf,
bag-size_wf,
bag-remove-repeats_wf,
nat_wf,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[b:bag(T)]. (bag-has-no-repeats(eq;b) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-08_08_56
Last ObjectModification:
2015_12_27-PM-04_13_00
Theory : bags_2
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