Nuprl Lemma : continuous-monotone-list
∀[F:Type ⟶ Type]. ContinuousMonotone(T.F[T] List) supposing ContinuousMonotone(T.F[T])
Proof
Definitions occuring in Statement :
list: T List,
continuous-monotone: ContinuousMonotone(T.F[T]),
uimplies: b supposing a,
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,
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
list: T List,
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
type-continuous: Continuous(T.F[T]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
colist_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type,
colength_wf,
subtype_rel_set,
subtype_rel_colist,
subtype_rel_wf,
strong-continuous-list,
subtype_rel_weakening,
list_wf,
continuous-monotone_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
independent_isectElimination,
intEquality,
natural_numberEquality,
cumulativity,
because_Cache,
productElimination,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isectEquality,
independent_pairEquality,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. ContinuousMonotone(T.F[T] List) supposing ContinuousMonotone(T.F[T])
Date html generated:
2016_05_14-PM-03_07_23
Last ObjectModification:
2015_12_26-PM-01_51_44
Theory : list_1
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