Nuprl Lemma : bsublist_weakening
∀s:DSet. ∀as,bs:|s| List.  ((as ≡(|s|) bs) 
⇒ (↑bsublist(s;as;bs)))
Proof
Definitions occuring in Statement : 
bsublist: bsublist(s;as;bs)
, 
permr: as ≡(T) bs
, 
list: T List
, 
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
, 
member: t ∈ T
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
dset: DSet
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
guard: {T}
, 
rev_implies: P 
⇐ Q
, 
squash: ↓T
, 
true: True
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
Lemmas referenced : 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
itermVar_wf, 
intformle_wf, 
intformnot_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
iff_weakening_equal, 
count_wf, 
true_wf, 
squash_wf, 
le_wf, 
count_bsublist, 
permr_iff_eq_counts_a, 
dset_wf, 
list_wf, 
set_car_wf, 
permr_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isectElimination, 
setElimination, 
rename, 
hypothesisEquality, 
hypothesis, 
productElimination, 
independent_functionElimination, 
because_Cache, 
applyEquality, 
lambdaEquality, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
intEquality, 
natural_numberEquality, 
sqequalRule, 
imageMemberEquality, 
baseClosed, 
universeEquality, 
independent_isectElimination, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
computeAll
Latex:
\mforall{}s:DSet.  \mforall{}as,bs:|s|  List.    ((as  \mequiv{}(|s|)  bs)  {}\mRightarrow{}  (\muparrow{}bsublist(s;as;bs)))
Date html generated:
2016_05_16-AM-07_41_40
Last ObjectModification:
2016_01_16-PM-11_11_50
Theory : list_2
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