Nuprl Lemma : indexed-F-bisimulation_wf
∀[I:Type]. ∀[F:Type ⟶ Type]. ∀[R:(I ⟶ corec(T.F[T])) ⟶ (I ⟶ corec(T.F[T])) ⟶ ℙ].
x,y.R[x;y] is an T.F[T]-bisimulation (indexed I) ∈ ℙ' supposing ContinuousMonotone(T.F[T])
Proof
Definitions occuring in Statement :
indexed-F-bisimulation: x,y.R[x; y] is an T.F[T]-bisimulation (indexed I),
corec: corec(T.F[T]),
continuous-monotone: ContinuousMonotone(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
indexed-F-bisimulation: x,y.R[x; y] is an T.F[T]-bisimulation (indexed I),
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
guard: {T},
continuous-monotone: ContinuousMonotone(T.F[T]),
type-monotone: Monotone(T.F[T]),
type-continuous: Continuous(T.F[T])
Lemmas referenced :
corec-ext,
all_wf,
subtype_rel_wf,
corec_wf,
subtype_rel_self,
equal_wf,
subtype_rel_transitivity,
subtype_rel_weakening,
continuous-monotone_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
hypothesis,
instantiate,
functionEquality,
productEquality,
functionExtensionality,
because_Cache,
cumulativity,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Type]. \mforall{}[F:Type {}\mrightarrow{} Type]. \mforall{}[R:(I {}\mrightarrow{} corec(T.F[T])) {}\mrightarrow{} (I {}\mrightarrow{} corec(T.F[T])) {}\mrightarrow{} \mBbbP{}].
x,y.R[x;y] is an T.F[T]-bisimulation (indexed I) \mmember{} \mBbbP{}' supposing ContinuousMonotone(T.F[T])
Date html generated:
2019_06_20-PM-00_37_17
Last ObjectModification:
2018_08_01-AM-10_46_04
Theory : co-recursion
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