Nuprl Lemma : continuous-monotone-id
ContinuousMonotone(T.T)
Proof
Definitions occuring in Statement :
continuous-monotone: ContinuousMonotone(T.F[T])
Definitions unfolded in proof :
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T])
Lemmas referenced :
subtype_rel_wf,
continuous-id,
subtype_rel_self,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalRule,
axiomEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isectEquality,
applyEquality,
functionEquality,
cumulativity
Latex:
ContinuousMonotone(T.T)
Date html generated:
2016_05_13-PM-04_10_16
Last ObjectModification:
2015_12_26-AM-11_22_15
Theory : subtype_1
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