Nuprl Lemma : uall_subtype
∀[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],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_apply: x[s]
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
universeEquality,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
functionEquality,
lambdaEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
cumulativity
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. \mforall{}[A:Type]. ((\mforall{}[A:Type]. F[A]) \msubseteq{}r F[A])
Date html generated:
2016_05_13-PM-03_07_08
Last ObjectModification:
2016_01_06-PM-05_28_33
Theory : core_2
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