Nuprl Lemma : general_corec_wf
∀[I:Type]. ∀[R:I ⟶ I ⟶ ℙ].
∀[F:Type ⟶ Type]. (general_corec(I;x,y.R[x;y];T.F[T]) ∈ Type) supposing tcWO(I;x,y.R[x;y])
Proof
Definitions occuring in Statement :
general_corec: general_corec(I;x,y.R[x; y];T.F[T]),
tcWO: tcWO(T;x,y.>[x; y]),
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,
general_corec: general_corec(I;x,y.R[x; y];T.F[T]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
iterate_functor_wf,
tcWO_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
isectEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
independent_isectElimination,
hypothesis,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
cumulativity
Latex:
\mforall{}[I:Type]. \mforall{}[R:I {}\mrightarrow{} I {}\mrightarrow{} \mBbbP{}].
\mforall{}[F:Type {}\mrightarrow{} Type]. (general\_corec(I;x,y.R[x;y];T.F[T]) \mmember{} Type) supposing tcWO(I;x,y.R[x;y])
Date html generated:
2016_05_14-AM-06_11_52
Last ObjectModification:
2015_12_26-PM-00_06_22
Theory : co-recursion
Home
Index