Nuprl Lemma : bsublist_functionality_wrt_permr
∀s:DSet. ∀as,bs,as',bs':|s| List.  ((as ≡(|s|) bs) 
⇒ (as' ≡(|s|) bs') 
⇒ bsublist(s;as;as') = bsublist(s;bs;bs'))
Proof
Definitions occuring in Statement : 
bsublist: bsublist(s;as;bs)
, 
permr: as ≡(T) bs
, 
list: T List
, 
bool: 𝔹
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
equal: s = t ∈ T
, 
dset: DSet
, 
set_car: |p|
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
dset: DSet
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
guard: {T}
, 
uimplies: b supposing a
, 
rev_implies: P 
⇐ Q
, 
true: True
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
permr_wf, 
set_car_wf, 
list_wf, 
dset_wf, 
permr_iff_eq_counts_a, 
iff_imp_equal_bool, 
bsublist_wf, 
count_bsublist_a, 
assert_wf, 
le_wf, 
count_wf, 
squash_wf, 
true_wf, 
istype-int, 
subtype_rel_self, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
hypothesis, 
universeIsType, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isectElimination, 
setElimination, 
rename, 
hypothesisEquality, 
inhabitedIsType, 
productElimination, 
independent_functionElimination, 
because_Cache, 
independent_isectElimination, 
independent_pairFormation, 
promote_hyp, 
sqequalRule, 
functionIsType, 
natural_numberEquality, 
applyEquality, 
lambdaEquality_alt, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
imageMemberEquality, 
baseClosed, 
instantiate, 
universeEquality
Latex:
\mforall{}s:DSet.  \mforall{}as,bs,as',bs':|s|  List.
    ((as  \mequiv{}(|s|)  bs)  {}\mRightarrow{}  (as'  \mequiv{}(|s|)  bs')  {}\mRightarrow{}  bsublist(s;as;as')  =  bsublist(s;bs;bs'))
Date html generated:
2019_10_16-PM-01_05_15
Last ObjectModification:
2018_10_08-PM-00_49_33
Theory : list_2
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