Nuprl Lemma : list-functor
∀[T:Type]. ContinuousMonotone(L.Unit ⋃ (T × L))
Proof
Definitions occuring in Statement :
continuous-monotone: ContinuousMonotone(T.F[T]),
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
unit: Unit,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
guard: {T},
ext-eq: A ≡ B,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
pi2: snd(t),
bfalse: ff,
top: Top,
pi1: fst(t)
Lemmas referenced :
subtype_rel_b-union,
unit_wf2,
subtype_rel_self,
subtype_rel_product,
subtype_rel_wf,
subtype_rel_weakening,
nat_wf,
b-union_wf,
decidable__equal_bool,
btrue_wf,
false_wf,
le_wf,
isaxiom_wf_listunion,
equal_wf,
ifthenelse_wf,
axiom-listunion,
bfalse_wf,
non-axiom-listunion,
bool_cases,
pair-eta,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productEquality,
cumulativity,
hypothesisEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
lambdaEquality,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isectEquality,
applyEquality,
functionExtensionality,
functionEquality,
instantiate,
productElimination,
independent_pairEquality,
dependent_functionElimination,
unionElimination,
dependent_set_memberEquality,
natural_numberEquality,
independent_functionElimination,
imageMemberEquality,
dependent_pairEquality,
baseClosed,
voidElimination,
voidEquality,
applyLambdaEquality
Latex:
\mforall{}[T:Type]. ContinuousMonotone(L.Unit \mcup{} (T \mtimes{} L))
Date html generated:
2017_04_14-AM-07_54_08
Last ObjectModification:
2017_02_27-PM-03_20_58
Theory : list_0
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