Nuprl Lemma : bar-wf-base
∀[T:Type]. bar(T) ∈ Type supposing T ⊆r Base
Proof
Definitions occuring in Statement :
bar: bar(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
bar: bar(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
base_wf,
subtype_rel_wf,
partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. bar(T) \mmember{} Type supposing T \msubseteq{}r Base
Date html generated:
2016_05_15-PM-10_03_41
Last ObjectModification:
2016_01_05-PM-06_24_33
Theory : bar!type
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