Nuprl Lemma : colist-fix-partial
∀[A:Type]
(∀[T:Type]. ∀[f:⋂L:Type. ((L ⟶ partial(A)) ⟶ (Unit ⋃ (T × L)) ⟶ partial(A))].
(fix(f) ∈ colist(T) ⟶ partial(A))) supposing
(mono(A) and
value-type(A))
Proof
Definitions occuring in Statement :
colist: colist(T),
partial: partial(T),
mono: mono(T),
value-type: value-type(T),
b-union: A ⋃ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
fix: fix(F),
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
colist: colist(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
fix_wf_corec-partial1,
b-union_wf,
unit_wf2,
list-functor,
partial_wf,
mono_wf,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
productEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
cumulativity,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]
(\mforall{}[T:Type]. \mforall{}[f:\mcap{}L:Type. ((L {}\mrightarrow{} partial(A)) {}\mrightarrow{} (Unit \mcup{} (T \mtimes{} L)) {}\mrightarrow{} partial(A))].
(fix(f) \mmember{} colist(T) {}\mrightarrow{} partial(A))) supposing
(mono(A) and
value-type(A))
Date html generated:
2016_05_14-AM-06_25_21
Last ObjectModification:
2015_12_26-PM-00_42_37
Theory : list_0
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