Nuprl Lemma : mk_mset_wf
∀s:DSet. ∀as:|s| List. (mk_mset(as) ∈ MSet{s})
Proof
Definitions occuring in Statement :
mk_mset: mk_mset(as),
mset: MSet{s},
list: T List,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
mk_mset: mk_mset(as),
mset: MSet{s},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
implies: P ⇒ Q
Lemmas referenced :
list_wf,
set_car_wf,
dset_wf,
quotient-member-eq,
permr_wf,
permr_equiv_rel,
permr_reflex
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_isectElimination,
because_Cache,
independent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}as:|s| List. (mk\_mset(as) \mmember{} MSet\{s\})
Date html generated:
2016_05_16-AM-07_46_17
Last ObjectModification:
2015_12_28-PM-06_04_04
Theory : mset
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