### Nuprl Lemma : int-prod_wf

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

Proof

Definitions occuring in Statement :  int-prod: `Π(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` int-prod: `Π(f[x] | x < k)` so_apply: `x[s]` nat: `ℕ`
Lemmas referenced :  primrec_wf int_seg_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin intEquality hypothesisEquality natural_numberEquality lambdaEquality multiplyEquality applyEquality setElimination rename hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache

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

Date html generated: 2016_05_14-AM-07_33_46
Last ObjectModification: 2015_12_26-PM-01_23_46

Theory : int_2

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