Nuprl Lemma : coterm-fun-continous
∀[opr:Type]. ContinuousMonotone(T.coterm-fun(opr;T))
Proof
Definitions occuring in Statement : 
coterm-fun: coterm-fun(opr;T)
, 
continuous-monotone: ContinuousMonotone(T.F[T])
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
coterm-fun: coterm-fun(opr;T)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
implies: P 
⇒ Q
, 
uimplies: b supposing a
, 
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])
Lemmas referenced : 
continuous-monotone-union, 
varname_wf, 
not_wf, 
equal-wf-T-base, 
list_wf, 
continuous-monotone-constant, 
continuous-monotone-product, 
continuous-monotone-list, 
continuous-monotone-id, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
lambdaEquality_alt, 
setEquality, 
hypothesis, 
isectElimination, 
hypothesisEquality, 
baseClosed, 
inhabitedIsType, 
productEquality, 
independent_functionElimination, 
independent_isectElimination, 
productElimination, 
independent_pairEquality, 
isect_memberEquality_alt, 
axiomEquality, 
isectIsTypeImplies, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  ContinuousMonotone(T.coterm-fun(opr;T))
Date html generated:
2020_05_19-PM-09_53_25
Last ObjectModification:
2020_03_09-PM-04_08_06
Theory : terms
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