Nuprl Lemma : continuous-monotone-function
∀[F:Type ⟶ Type]. ∀[A:Type]. ContinuousMonotone(T.A ⟶ F[T]) supposing ContinuousMonotone(T.F[T])
Proof
Definitions occuring in Statement : 
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
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s]
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
continuous-monotone: ContinuousMonotone(T.F[T])
, 
and: P ∧ Q
, 
type-monotone: Monotone(T.F[T])
, 
subtype_rel: A ⊆r B
, 
type-continuous: Continuous(T.F[T])
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
Lemmas referenced : 
continuous-monotone-depfunction, 
subtype_rel_wf, 
nat_wf, 
continuous-monotone_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
applyEquality, 
universeEquality, 
independent_isectElimination, 
lambdaFormation, 
hypothesis, 
because_Cache, 
productElimination, 
independent_pairEquality, 
isect_memberEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
cumulativity
Latex:
\mforall{}[F:Type  {}\mrightarrow{}  Type].  \mforall{}[A:Type].  ContinuousMonotone(T.A  {}\mrightarrow{}  F[T])  supposing  ContinuousMonotone(T.F[T])
Date html generated:
2016_05_13-PM-04_09_48
Last ObjectModification:
2015_12_26-AM-11_22_33
Theory : subtype_1
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