Nuprl Lemma : fin_type_properties
∀s:DSet. ∀as:|s| List. ∀a:{as}. (↑(a ∈b as))
Proof
Definitions occuring in Statement :
fin_type: {as},
mem: a ∈b as,
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
fin_type: {as},
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
dset: DSet
Lemmas referenced :
dset_wf,
set_car_wf,
list_wf,
fin_type_wf,
decidable__assert,
mem_wf,
assert_wf,
sq_stable_from_decidable
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
isectElimination,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
introduction,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}s:DSet. \mforall{}as:|s| List. \mforall{}a:\{as\}. (\muparrow{}(a \mmember{}\msubb{} as))
Date html generated:
2016_05_16-AM-07_42_44
Last ObjectModification:
2016_01_16-PM-11_12_01
Theory : list_2
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