Nuprl Lemma : m-corec_wf
∀[k:ℕ]. ∀[F:(ℕk ⟶ Type) ⟶ ℕk ⟶ Type]. ∀[i:ℕk]. (m-corec(T.F[T];i) ∈ Type)
Proof
Definitions occuring in Statement :
m-corec: m-corec(T.F[T];i),
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,
m-corec: m-corec(T.F[T];i),
nat: ℕ
Lemmas referenced :
mutual-corec_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[F:(\mBbbN{}k {}\mrightarrow{} Type) {}\mrightarrow{} \mBbbN{}k {}\mrightarrow{} Type]. \mforall{}[i:\mBbbN{}k]. (m-corec(T.F[T];i) \mmember{} Type)
Date html generated:
2018_05_21-PM-00_17_45
Last ObjectModification:
2017_10_18-PM-02_45_50
Theory : co-recursion
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