Nuprl Lemma : int-prod_wf_nat
∀[n:ℕ]. ∀[f:ℕn ⟶ ℕ]. (Π(f[x] | x < n) ∈ ℕ)
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-prod: Π(f[x] | x < k),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
primrec_wf,
nat_wf,
false_wf,
le_wf,
mul_bounds_1a,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
lambdaEquality,
multiplyEquality,
setElimination,
rename,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}]. (\mPi{}(f[x] | x < n) \mmember{} \mBbbN{})
Date html generated:
2016_05_14-AM-07_33_49
Last ObjectModification:
2015_12_26-PM-01_23_43
Theory : int_2
Home
Index