### 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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