Nuprl Lemma : mem_bsublist_imp
∀s:DSet. ∀as,bs:|s| List. ((↑bsublist(s;as;bs)) ⇒ (∀c:|s|. ((↑(c ∈b as)) ⇒ (↑(c ∈b bs)))))
Proof
Definitions occuring in Statement :
bsublist: bsublist(s;as;bs),
mem: a ∈b as,
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,
gt: i > j,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
dset: DSet,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top
Lemmas referenced :
gt_wf,
count_wf,
set_car_wf,
le_wf,
count_bsublist_a,
mem_iff_count_nzero,
assert_wf,
mem_wf,
bsublist_wf,
list_wf,
dset_wf,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
sqequalRule,
functionIsType,
independent_functionElimination,
productElimination,
because_Cache,
inhabitedIsType,
unionElimination,
independent_isectElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. ((\muparrow{}bsublist(s;as;bs)) {}\mRightarrow{} (\mforall{}c:|s|. ((\muparrow{}(c \mmember{}\msubb{} as)) {}\mRightarrow{} (\muparrow{}(c \mmember{}\msubb{} bs)))))
Date html generated:
2019_10_16-PM-01_05_08
Last ObjectModification:
2018_10_08-AM-11_44_31
Theory : list_2
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