Nuprl Lemma : F-bisimulation_wf
∀[F:Type ⟶ Type]. ∀[R:corec(T.F[T]) ⟶ corec(T.F[T]) ⟶ ℙ].
x,y.R[x;y] is an T.F[T]-bisimulation ∈ ℙ' supposing ContinuousMonotone(T.F[T])
Proof
Definitions occuring in Statement :
F-bisimulation: x,y.R[x; y] is an T.F[T]-bisimulation,
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],
F-bisimulation: x,y.R[x; y] is an T.F[T]-bisimulation,
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
cand: A c∧ B,
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{}[F:Type {}\mrightarrow{} Type]. \mforall{}[R:corec(T.F[T]) {}\mrightarrow{} corec(T.F[T]) {}\mrightarrow{} \mBbbP{}].
x,y.R[x;y] is an T.F[T]-bisimulation \mmember{} \mBbbP{}' supposing ContinuousMonotone(T.F[T])
Date html generated:
2019_06_20-PM-00_37_09
Last ObjectModification:
2018_08_07-PM-02_08_29
Theory : co-recursion
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