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
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