Nuprl Lemma : type-monotone-union-continuous
∀[F:Type ⟶ Type]. union-continuous{i:l}(T.F[T]) supposing Monotone(T.F[T])
Proof
Definitions occuring in Statement :
union-continuous: union-continuous{i:l}(T.F[T]),
type-monotone: Monotone(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
union-continuous: union-continuous{i:l}(T.F[T]),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
tunion: ⋃x:A.B[x],
pi2: snd(t),
type-monotone: Monotone(T.F[T])
Lemmas referenced :
type-monotone_wf,
tunion_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
applyEquality,
hypothesis,
axiomEquality,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
imageElimination,
productElimination,
independent_isectElimination,
imageMemberEquality,
dependent_pairEquality,
baseClosed
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. union-continuous\{i:l\}(T.F[T]) supposing Monotone(T.F[T])
Date html generated:
2016_05_13-PM-04_10_20
Last ObjectModification:
2016_01_14-PM-07_29_47
Theory : subtype_1
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