Nuprl Lemma : continuous'-monotone-constant
∀[A:Type]. continuous'-monotone{i:l}(T.A)
Proof
Definitions occuring in Statement :
continuous'-monotone: continuous'-monotone{i:l}(T.F[T]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
continuous'-monotone: continuous'-monotone{i:l}(T.F[T]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
type-monotone: Monotone(T.F[T]),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
type-continuous': semi-continuous(λT.F[T]),
tunion: ⋃x:A.B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
pi2: snd(t)
Lemmas referenced :
type-incr-chain_wf,
le_wf,
false_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
hypothesisEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_pairFormation,
imageMemberEquality,
dependent_pairEquality,
dependent_set_memberEquality,
natural_numberEquality,
lambdaFormation,
cumulativity,
baseClosed,
productElimination,
independent_pairEquality
Latex:
\mforall{}[A:Type]. continuous'-monotone\{i:l\}(T.A)
Date html generated:
2016_05_15-PM-06_53_38
Last ObjectModification:
2016_01_16-AM-09_48_27
Theory : general
Home
Index