Nuprl Lemma : mem_wf
∀s:DSet. ∀a:|s|. ∀bs:|s| List. (a ∈b bs ∈ 𝔹)
Proof
Definitions occuring in Statement :
mem: a ∈b as,
list: T List,
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
mem: a ∈b as,
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
dset: DSet,
so_lambda: λ2x.t[x],
infix_ap: x f y,
bor_mon: <𝔹,∨b>,
grp_car: |g|,
pi1: fst(t),
so_apply: x[s],
abmonoid: AbMon,
mon: Mon
Lemmas referenced :
mon_for_wf,
bor_mon_wf,
iabmonoid_subtype_imon,
abmonoid_subtype_iabmonoid,
subtype_rel_transitivity,
abmonoid_wf,
iabmonoid_wf,
imon_wf,
set_car_wf,
set_eq_wf,
bool_wf,
grp_car_wf,
list_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
setElimination,
rename,
hypothesisEquality,
lambdaEquality
Latex:
\mforall{}s:DSet. \mforall{}a:|s|. \mforall{}bs:|s| List. (a \mmember{}\msubb{} bs \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-07_36_52
Last ObjectModification:
2015_12_28-PM-05_45_08
Theory : list_2
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