Nuprl Lemma : isect-subtype-1
∀[F:Type ⟶ Type]. ∀[A:Type]. ((⋂A:Type. F[A]) ⊆r F[A])
Proof
Definitions occuring in Statement :
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
subtype_rel: A ⊆r B
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis,
isectEquality,
universeEquality,
cumulativity,
applyEquality,
axiomEquality,
sqequalHypSubstitution,
isect_memberEquality,
thin,
because_Cache,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. \mforall{}[A:Type]. ((\mcap{}A:Type. F[A]) \msubseteq{}r F[A])
Date html generated:
2016_05_15-PM-03_21_26
Last ObjectModification:
2015_12_27-PM-01_04_12
Theory : general
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