Nuprl Lemma : corec-subtype
∀[F:Type ⟶ Type]. corec(T.F[T]) ⊆r F[corec(T.F[T])] supposing Continuous(T.F[T])
Proof
Definitions occuring in Statement :
corec: corec(T.F[T]),
type-continuous: Continuous(T.F[T]),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
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],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
corec_subtype,
type-continuous_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
hypothesis,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. corec(T.F[T]) \msubseteq{}r F[corec(T.F[T])] supposing Continuous(T.F[T])
Date html generated:
2016_05_14-AM-06_24_43
Last ObjectModification:
2015_12_26-AM-11_58_15
Theory : co-recursion
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