Nuprl Lemma : bag-covers_wf

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[cvr,b:bag(T)].  (bag-covers(T;R;cvr;b) ∈ ℙ)


Proof




Definitions occuring in Statement :  bag-covers: bag-covers(T;R;cvr;b) bag: bag(T) uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T bag-covers: bag-covers(T;R;cvr;b) so_lambda: λ2x.t[x] implies:  Q prop: infix_ap: y so_apply: x[s]
Lemmas referenced :  all_wf bag-member_wf or_wf exists_wf and_wf bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality hypothesis applyEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[cvr,b:bag(T)].    (bag-covers(T;R;cvr;b)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_15-PM-03_12_23
Last ObjectModification: 2015_12_27-AM-09_23_29

Theory : bags


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