Nuprl Lemma : continuous-monotone-union
∀F,G:Type ⟶ Type. (ContinuousMonotone(T.F[T])
⇒ ContinuousMonotone(T.G[T])
⇒ ContinuousMonotone(T.F[T] + G[T]))
Proof
Definitions occuring in Statement :
continuous-monotone: ContinuousMonotone(T.F[T])
,
so_apply: x[s]
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
function: x:A ⟶ B[x]
,
union: left + right
,
universe: Type
Definitions unfolded in proof :
so_apply: x[s]
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
continuous-monotone: ContinuousMonotone(T.F[T])
,
and: P ∧ Q
,
type-monotone: Monotone(T.F[T])
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
type-continuous: Continuous(T.F[T])
,
subtype_rel: A ⊆r B
,
so_lambda: λ2x.t[x]
,
strong-type-continuous: Continuous+(T.F[T])
,
ext-eq: A ≡ B
,
guard: {T}
,
prop: ℙ
Lemmas referenced :
subtype_rel_sum,
subtype_rel_wf,
strong-continuous-union,
nat_wf,
subtype_rel_weakening,
continuous-monotone_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
lambdaEquality,
isectEquality,
independent_pairEquality,
functionEquality,
cumulativity,
unionEquality
Latex:
\mforall{}F,G:Type {}\mrightarrow{} Type.
(ContinuousMonotone(T.F[T]) {}\mRightarrow{} ContinuousMonotone(T.G[T]) {}\mRightarrow{} ContinuousMonotone(T.F[T] + G[T]))
Date html generated:
2016_05_13-PM-04_10_10
Last ObjectModification:
2015_12_26-AM-11_22_20
Theory : subtype_1
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