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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