Nuprl Lemma : oal_merge_wf
∀a:LOSet. ∀b:AbDMon. ∀ps,qs:(|a| × |b|) List. (ps ++ qs ∈ (|a| × |b|) List)
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
list: T List,
all: ∀x:A. B[x],
member: t ∈ T,
product: x:A × B[x],
abdmonoid: AbDMon,
grp_car: |g|,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
pi1: fst(t),
pi2: snd(t),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
oal_merge: ps ++ qs,
ycomb: Y,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
bnot: ¬bb,
assert: ↑b,
infix_ap: x f y
Lemmas referenced :
abdmonoid_wf,
loset_wf,
list_wf,
set_car_wf,
grp_car_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
product_subtype_list,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
equal_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
null_nil_lemma,
reduce_tl_nil_lemma,
oal_merge_left_nil_lemma,
null_cons_lemma,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
oal_merge_right_nil_lemma,
cons_wf,
set_blt_wf,
bool_wf,
eqtt_to_assert,
assert_of_set_lt,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
set_lt_wf,
infix_ap_wf,
grp_eq_wf,
grp_op_wf,
grp_id_wf,
assert_of_mon_eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
productEquality,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
because_Cache,
productElimination,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
unionElimination,
promote_hyp,
hypothesis_subsumption,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
baseClosed,
instantiate,
cumulativity,
imageElimination,
independent_pairEquality,
equalityElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps,qs:(|a| \mtimes{} |b|) List. (ps ++ qs \mmember{} (|a| \mtimes{} |b|) List)
Date html generated:
2017_10_01-AM-10_02_28
Last ObjectModification:
2017_03_03-PM-01_05_04
Theory : polynom_2
Home
Index