Nuprl Lemma : b-union_wf
∀[A,B:Type]. (A ⋃ B ∈ Type)
Proof
Definitions occuring in Statement :
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
tunion_wf,
bool_wf,
ifthenelse_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
instantiate,
hypothesisEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. (A \mcup{} B \mmember{} Type)
Date html generated:
2016_05_13-PM-03_20_59
Last ObjectModification:
2015_12_26-AM-09_10_35
Theory : union
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