Nuprl Lemma : mem_lmax
∀s:DSet. ∀as,bs:|s| List. ∀c:|s|. c ∈b lmax(s;as;bs) = (c ∈b as) ∨b(c ∈b bs)
Proof
Definitions occuring in Statement :
lmax: lmax(s;as;bs),
mem: a ∈b as,
list: T List,
bor: p ∨bq,
bool: 𝔹,
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
gt: i > j,
or: P ∨ Q,
dset: DSet,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
le: A ≤ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
mem_wf,
lmax_wf,
bor_wf,
assert_wf,
gt_wf,
count_wf,
or_wf,
set_car_wf,
list_wf,
dset_wf,
iff_imp_equal_bool,
mem_iff_count_nzero,
iff_weakening_uiff,
assert_of_bor,
le_int_wf,
equal-wf-T-base,
bool_wf,
le_wf,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_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_wf,
intformle_wf,
int_formula_prop_le_lemma,
lt_int_wf,
less_than_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
imax_unfold,
iff_weakening_equal,
imax_wf,
squash_wf,
true_wf,
count_lmax,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
because_Cache,
universeIsType,
natural_numberEquality,
sqequalRule,
unionIsType,
setElimination,
rename,
inhabitedIsType,
lambdaFormation_alt,
independent_isectElimination,
productElimination,
independent_functionElimination,
unionElimination,
inlFormation_alt,
inrFormation_alt,
independent_pairFormation,
promote_hyp,
equalityTransitivity,
equalitySymmetry,
baseClosed,
imageElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
equalityElimination,
equalityIsType1,
applyEquality,
imageMemberEquality,
instantiate,
universeEquality
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. \mforall{}c:|s|. c \mmember{}\msubb{} lmax(s;as;bs) = (c \mmember{}\msubb{} as) \mvee{}\msubb{}(c \mmember{}\msubb{} bs)
Date html generated:
2019_10_16-PM-01_04_47
Last ObjectModification:
2018_10_08-AM-10_14_55
Theory : list_2
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