Nuprl Lemma : sum_wf

`∀[n:ℕ]. ∀[f:ℕn ⟶ ℤ].  (Σ(f[x] | x < n) ∈ ℤ)`

Proof

Definitions occuring in Statement :  sum: `Σ(f[x] | x < k)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` sum: `Σ(f[x] | x < k)` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  nat_wf int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le nat_properties int_seg_wf sum_aux_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality because_Cache setElimination rename hypothesisEquality hypothesis lambdaEquality applyEquality independent_isectElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll axiomEquality equalityTransitivity equalitySymmetry functionEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f:\mBbbN{}n  {}\mrightarrow{}  \mBbbZ{}].    (\mSigma{}(f[x]  |  x  <  n)  \mmember{}  \mBbbZ{})

Date html generated: 2016_05_14-AM-07_31_17
Last ObjectModification: 2016_01_14-PM-09_56_52

Theory : int_2

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