Nuprl Lemma : fin_type_inc
∀s:DSet. ∀as,bs:|s| List. ((↑bsublist(s;as;bs)) ⇒ ({as} ⊆r {bs}))
Proof
Definitions occuring in Statement :
fin_type: {as},
bsublist: bsublist(s;as;bs),
list: T List,
assert: ↑b,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
dset: DSet,
fin_type: {as}
Lemmas referenced :
fin_type_wf,
assert_wf,
bsublist_wf,
list_wf,
set_car_wf,
dset_wf,
mem_wf,
fin_type_properties,
mem_bsublist_imp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename,
dependent_set_memberEquality,
independent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. ((\muparrow{}bsublist(s;as;bs)) {}\mRightarrow{} (\{as\} \msubseteq{}r \{bs\}))
Date html generated:
2019_10_16-PM-01_05_42
Last ObjectModification:
2018_09_17-PM-06_19_44
Theory : list_2
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