Nuprl Lemma : continuous'-monotone-sum
∀[F,G:Type ⟶ Type].
  (continuous'-monotone{i:l}(T.F[T] + G[T])) supposing 
     (continuous'-monotone{i:l}(T.G[T]) and 
     continuous'-monotone{i:l}(T.F[T]))
Proof
Definitions occuring in Statement : 
continuous'-monotone: continuous'-monotone{i:l}(T.F[T])
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
function: x:A ⟶ B[x]
, 
union: left + right
, 
universe: Type
Definitions unfolded in proof : 
so_apply: x[s]
, 
continuous'-monotone: continuous'-monotone{i:l}(T.F[T])
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
type-monotone: Monotone(T.F[T])
, 
subtype_rel: A ⊆r B
, 
type-continuous': semi-continuous(λT.F[T])
, 
so_lambda: λ2x.t[x]
, 
type-incr-chain: type-incr-chain{i:l}()
, 
tunion: ⋃x:A.B[x]
, 
pi2: snd(t)
, 
prop: ℙ
Lemmas referenced : 
type-continuous'_wf, 
type-monotone_wf, 
and_wf, 
type-incr-chain_wf, 
nat_wf, 
tunion_wf, 
subtype_rel_union, 
subtype_rel_wf, 
subtype_rel_sum
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
lemma_by_obid, 
isectElimination, 
applyEquality, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
axiomEquality, 
isect_memberEquality, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
independent_pairFormation, 
lambdaEquality, 
setElimination, 
rename, 
unionElimination, 
imageElimination, 
imageMemberEquality, 
dependent_pairEquality, 
inlEquality, 
unionEquality, 
baseClosed, 
inrEquality, 
independent_pairEquality, 
instantiate, 
functionEquality
Latex:
\mforall{}[F,G:Type  {}\mrightarrow{}  Type].
    (continuous'-monotone\{i:l\}(T.F[T]  +  G[T]))  supposing 
          (continuous'-monotone\{i:l\}(T.G[T])  and 
          continuous'-monotone\{i:l\}(T.F[T]))
Date html generated:
2016_05_15-PM-06_53_25
Last ObjectModification:
2016_01_16-AM-09_49_02
Theory : general
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