Nuprl Lemma : W_corec_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[F:Type ⟶ Type]. (W_corec(A;a.B[a];T.F[T]) ∈ Type)
Proof
Definitions occuring in Statement :
W_corec: W_corec(A;a.B[a];T.F[T]),
uall: ∀[x:A]. B[x],
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,
W_corec: W_corec(A;a.B[a];T.F[T]),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
W_wf,
W_iterate_functor_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
isectEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
cumulativity
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[F:Type {}\mrightarrow{} Type]. (W\_corec(A;a.B[a];T.F[T]) \mmember{} Type)
Date html generated:
2016_05_14-AM-06_16_32
Last ObjectModification:
2015_12_26-PM-00_04_24
Theory : co-recursion
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