Nuprl Lemma : continuous-monotone-constant
∀[G:Type]. ContinuousMonotone(T.G)
Proof
Definitions occuring in Statement :
continuous-monotone: ContinuousMonotone(T.F[T]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
guard: {T}
Lemmas referenced :
subtype_rel_wf,
continuous-constant,
subtype_rel_weakening,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
hypothesisEquality,
sqequalRule,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isectEquality,
independent_isectElimination,
functionEquality,
cumulativity,
productElimination,
independent_pairEquality
Latex:
\mforall{}[G:Type]. ContinuousMonotone(T.G)
Date html generated:
2016_05_13-PM-04_10_14
Last ObjectModification:
2015_12_26-AM-11_22_18
Theory : subtype_1
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