Nuprl Lemma : subtype-top
∀[T:Type]. uiff(T ⊆r Top;True)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
true: True,
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ
Lemmas referenced :
subtype_rel_wf,
top_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
natural_numberEquality,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_pairEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. uiff(T \msubseteq{}r Top;True)
Date html generated:
2016_05_13-PM-03_19_13
Last ObjectModification:
2015_12_26-AM-09_07_50
Theory : subtype_0
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