`∀[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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