Nuprl Lemma : subtype_rel_b-union-left
∀[A,B:Type]. (A ⊆r (A ⋃ B))
Proof
Definitions occuring in Statement :
b-union: A ⋃ B,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
pi2: snd(t)
Lemmas referenced :
btrue_wf,
ifthenelse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalRule,
imageMemberEquality,
dependent_pairEquality,
lemma_by_obid,
hypothesis,
hypothesisEquality,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
universeEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. (A \msubseteq{}r (A \mcup{} B))
Date html generated:
2016_05_13-PM-03_57_47
Last ObjectModification:
2015_12_26-AM-10_51_26
Theory : bool_1
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