Nuprl Lemma : bsublist_functionality_wrt_bsublist
∀s:DSet. ∀as,as',bs,bs':|s| List.
((↑bsuplist(s;as;bs)) ⇒ (↑bsublist(s;as';bs')) ⇒ (↑(bsublist(s;as;as') ⇒b bsublist(s;bs;bs'))))
Proof
Definitions occuring in Statement :
bsuplist: bsuplist(s;as;bs),
bsublist: bsublist(s;as;bs),
list: T List,
bimplies: p ⇒b q,
assert: ↑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,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
dset: DSet,
bsuplist: bsuplist(s;as;bs),
guard: {T}
Lemmas referenced :
iff_weakening_uiff,
assert_wf,
bimplies_wf,
bsublist_wf,
isect_wf,
assert_of_bimplies,
assert_witness,
bsuplist_wf,
list_wf,
set_car_wf,
dset_wf,
bsublist_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality_alt,
because_Cache,
universeIsType,
lambdaEquality_alt,
independent_functionElimination,
productElimination,
isect_memberFormation_alt,
inhabitedIsType,
setElimination,
rename
Latex:
\mforall{}s:DSet. \mforall{}as,as',bs,bs':|s| List.
((\muparrow{}bsuplist(s;as;bs)) {}\mRightarrow{} (\muparrow{}bsublist(s;as';bs')) {}\mRightarrow{} (\muparrow{}(bsublist(s;as;as') {}\mRightarrow{}\msubb{} bsublist(s;bs;bs'))))
Date html generated:
2019_10_16-PM-01_05_18
Last ObjectModification:
2018_10_08-PM-05_45_38
Theory : list_2
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