Nuprl Lemma : bag-cover_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[cvr,b:bag(T)].  (bag-cover(T;R;cvr;b) ∈ ℙ)
Proof
Definitions occuring in Statement : 
bag-cover: bag-cover(T;R;mx;b)
, 
bag: bag(T)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bag-cover: bag-cover(T;R;mx;b)
, 
prop: ℙ
Lemmas referenced : 
and_wf, 
sub-bag_wf, 
bag-covers_wf, 
bag-incomparable_wf, 
bag_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
functionEquality, 
cumulativity, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[cvr,b:bag(T)].    (bag-cover(T;R;cvr;b)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-03_12_33
Last ObjectModification:
2015_12_27-AM-09_23_23
Theory : bags
Home
Index