Nuprl Lemma : mutual-corec_wf
∀[k:ℕ]. ∀[F:(ℕk ⟶ Type) ⟶ ℕk ⟶ Type]. (mutual-corec(T.F[T]) ∈ ℕk ⟶ Type)
Proof
Definitions occuring in Statement :
mutual-corec: mutual-corec(T.F[T]),
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,
mutual-corec: mutual-corec(T.F[T]),
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
k-intersection_wf,
primrec_wf,
int_seg_wf,
top_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
instantiate,
functionEquality,
cumulativity,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
universeEquality,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[F:(\mBbbN{}k {}\mrightarrow{} Type) {}\mrightarrow{} \mBbbN{}k {}\mrightarrow{} Type]. (mutual-corec(T.F[T]) \mmember{} \mBbbN{}k {}\mrightarrow{} Type)
Date html generated:
2018_05_21-PM-00_10_27
Last ObjectModification:
2017_10_18-PM-02_41_59
Theory : co-recursion
Home
Index