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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