Nuprl Lemma : function-subtype-top
∀[A,B:Type]. ((A ⟶ B) ⊆r Top)
Proof
Definitions occuring in Statement :
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
top: Top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
hypothesisEquality,
sqequalRule,
axiomEquality,
because_Cache,
universeEquality,
sqequalHypSubstitution,
isectElimination,
thin
Latex:
\mforall{}[A,B:Type]. ((A {}\mrightarrow{} B) \msubseteq{}r Top)
Date html generated:
2016_05_13-PM-04_10_48
Last ObjectModification:
2015_12_26-AM-11_21_50
Theory : subtype_1
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