Nuprl Lemma : reg-seq-list-add-as-l_sum
∀[L:(ℕ+ ⟶ ℤ) List]. (reg-seq-list-add(L) = (λn.l_sum(map(λx.(x n);L))) ∈ (ℕ+ ⟶ ℤ))
Proof
Definitions occuring in Statement :
reg-seq-list-add: reg-seq-list-add(L),
l_sum: l_sum(L),
map: map(f;as),
list: T List,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
reg-seq-list-add: reg-seq-list-add(L),
member: t ∈ T,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
l_sum_as_accum,
cbv_list_accum-is-list_accum,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_plus_properties,
int-value-type,
list_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lambdaEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
intEquality,
hypothesisEquality,
natural_numberEquality,
addEquality,
applyEquality,
setElimination,
rename,
dependent_functionElimination,
because_Cache,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll
Latex:
\mforall{}[L:(\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}) List]. (reg-seq-list-add(L) = (\mlambda{}n.l\_sum(map(\mlambda{}x.(x n);L))))
Date html generated:
2016_05_18-AM-06_48_08
Last ObjectModification:
2016_01_17-AM-01_45_12
Theory : reals
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