Nuprl Lemma : bag-rep_wf
∀[T:Type]. ∀[n:ℕ]. ∀[x:T]. (bag-rep(n;x) ∈ T List)
Proof
Definitions occuring in Statement :
bag-rep: bag-rep(n;x),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-rep: bag-rep(n;x),
empty-bag: {},
nil: [],
it: ⋅,
cons-bag: x.b,
nat: ℕ
Lemmas referenced :
primrec_wf,
list_wf,
nil_wf,
cons_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[x:T]. (bag-rep(n;x) \mmember{} T List)
Date html generated:
2016_05_15-PM-02_34_02
Last ObjectModification:
2015_12_27-AM-09_46_54
Theory : bags
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