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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