Nuprl Lemma : reg-seq-list-add_wf
∀[L:ℝ List]. (reg-seq-list-add(L) ∈ {f:ℕ+ ⟶ ℤ| ||L||-regular-seq(f)} )
Proof
Definitions occuring in Statement :
reg-seq-list-add: reg-seq-list-add(L),
real: ℝ,
regular-int-seq: k-regular-seq(f),
length: ||as||,
list: T List,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
reg-seq-list-add: reg-seq-list-add(L),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
real: ℝ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
nat_plus: ℕ+,
top: Top,
compose: f o g,
nat: ℕ,
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
sq_type: SQType(T),
int_lower: {...i},
sq_stable: SqStable(P)
Lemmas referenced :
le_wf,
sq_stable__le,
l_sum-upper-bound-map,
int_formula_prop_wf,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
itermMultiply_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_plus_properties,
int_subtype_base,
subtype_base_sq,
le_weakening,
l_sum-triangle-inequality,
le_functionality,
map-map,
nat_wf,
l_sum_wf,
subtract_wf,
absval_wf,
map_wf,
l_sum-mul-left,
iff_weakening_equal,
reg-seq-list-add-as-l_sum,
true_wf,
squash_wf,
int-value-type,
subtype_rel_list,
nat_plus_wf,
cbv_list_accum_wf,
list_wf,
real_wf,
length_wf,
regular-int-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
functionEquality,
intEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
natural_numberEquality,
addEquality,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
multiplyEquality,
dependent_functionElimination,
instantiate,
cumulativity,
unionElimination,
dependent_pairFormation,
int_eqEquality,
computeAll
Latex:
\mforall{}[L:\mBbbR{} List]. (reg-seq-list-add(L) \mmember{} \{f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| ||L||-regular-seq(f)\} )
Date html generated:
2016_05_18-AM-06_48_12
Last ObjectModification:
2016_01_17-AM-01_45_46
Theory : reals
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