Nuprl Lemma : k-intersection_wf
∀[k:ℕ]. ∀[X:ℕ ⟶ ℕk ⟶ Type]. (⋂n. X[n] ∈ ℕk ⟶ Type)
Proof
Definitions occuring in Statement :
k-intersection: ⋂n. X[n],
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,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
k-intersection: ⋂n. X[n],
so_apply: x[s],
nat: ℕ
Lemmas referenced :
nat_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
isectEquality,
extract_by_obid,
hypothesis,
applyEquality,
functionExtensionality,
hypothesisEquality,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[X:\mBbbN{} {}\mrightarrow{} \mBbbN{}k {}\mrightarrow{} Type]. (\mcap{}n. X[n] \mmember{} \mBbbN{}k {}\mrightarrow{} Type)
Date html generated:
2018_05_21-PM-00_09_17
Last ObjectModification:
2017_10_18-PM-02_33_49
Theory : co-recursion
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