Nuprl Lemma : isect_subtype_rel
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[x:A]. ((⋂x:A. B[x]) ⊆r B[x])
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,
applyEquality,
axiomEquality,
sqequalHypSubstitution,
isect_memberEquality,
thin,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:A]. ((\mcap{}x:A. B[x]) \msubseteq{}r B[x])
Date html generated:
2016_05_13-PM-03_18_59
Last ObjectModification:
2015_12_26-AM-09_07_59
Theory : subtype_0
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