Nuprl Lemma : l_sum-upper-bound-map
∀[b:ℤ]. ∀[T:Type]. ∀[f:T ⟶ {...b}]. ∀[L:T List].  (l_sum(map(f;L)) ≤ (b * ||L||))
Proof
Definitions occuring in Statement : 
l_sum: l_sum(L)
, 
length: ||as||
, 
map: map(f;as)
, 
list: T List
, 
int_lower: {...i}
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
function: x:A ⟶ B[x]
, 
multiply: n * m
, 
int: ℤ
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
top: Top
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
, 
le: A ≤ B
, 
and: P ∧ Q
, 
not: ¬A
, 
false: False
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
int_lower: {...i}
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
Lemmas referenced : 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermVar_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
int_lower_properties, 
l_member_wf, 
le_wf, 
l_all_iff, 
list_wf, 
int_lower_wf, 
subtype_rel_dep_function, 
l_sum_wf, 
length_wf, 
less_than'_wf, 
map_wf, 
l_sum-upper-bound, 
map-length
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
dependent_functionElimination, 
hypothesisEquality, 
intEquality, 
applyEquality, 
because_Cache, 
sqequalRule, 
independent_functionElimination, 
productElimination, 
independent_pairEquality, 
lambdaEquality, 
multiplyEquality, 
independent_isectElimination, 
lambdaFormation, 
setElimination, 
rename, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
universeEquality, 
setEquality, 
unionElimination, 
natural_numberEquality, 
dependent_pairFormation, 
int_eqEquality, 
independent_pairFormation, 
computeAll
Latex:
\mforall{}[b:\mBbbZ{}].  \mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  \{...b\}].  \mforall{}[L:T  List].    (l\_sum(map(f;L))  \mleq{}  (b  *  ||L||))
Date html generated:
2016_05_14-PM-02_51_40
Last ObjectModification:
2016_01_15-AM-07_32_31
Theory : list_1
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