Nuprl Lemma : subtype_rel_tagged+_general
∀[T,A,B:Type]. ∀[z:Atom]. (T ⊆r A |+ z:B) supposing ((T ⊆r z:B) and (T ⊆r A))
Proof
Definitions occuring in Statement :
tagged+: T |+ z:B,
tag-case: z:T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
tagged+: T |+ z:B,
isect2: T1 ⋂ T2,
subtype_rel: A ⊆r B,
ifthenelse: if b then t else f fi ,
bool: 𝔹
Lemmas referenced :
bool_wf,
subtype_rel_wf,
tag-case_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
isect_memberEquality,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
unionElimination,
thin,
hypothesis,
lemma_by_obid,
axiomEquality,
isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
atomEquality,
universeEquality
Latex:
\mforall{}[T,A,B:Type]. \mforall{}[z:Atom]. (T \msubseteq{}r A |+ z:B) supposing ((T \msubseteq{}r z:B) and (T \msubseteq{}r A))
Date html generated:
2016_05_15-PM-06_46_30
Last ObjectModification:
2015_12_27-AM-11_49_15
Theory : general
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