Nuprl Lemma : b-union-void
∀[V,T:Type]. ((V ⋃ T) ⊆r T) ∧ ((T ⋃ V) ⊆r T) supposing ¬V
Proof
Definitions occuring in Statement :
b-union: A ⋃ B,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
b-union_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
independent_functionElimination,
hypothesis,
voidElimination,
hypothesisEquality,
lemma_by_obid,
isectElimination,
independent_pairFormation,
independent_pairEquality,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[V,T:Type]. ((V \mcup{} T) \msubseteq{}r T) \mwedge{} ((T \mcup{} V) \msubseteq{}r T) supposing \mneg{}V
Date html generated:
2016_05_13-PM-04_10_09
Last ObjectModification:
2015_12_26-AM-11_22_31
Theory : subtype_1
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