Nuprl Lemma : l_contains_wf

[T:Type]. ∀[A,B:T List].  (A ⊆ B ∈ ℙ)


Proof




Definitions occuring in Statement :  l_contains: A ⊆ B list: List uall: [x:A]. B[x] prop: member: t ∈ T universe: Type
Definitions unfolded in proof :  l_contains: A ⊆ B uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] prop: so_apply: x[s]
Lemmas referenced :  l_all_wf l_member_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality setElimination rename hypothesis setEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[A,B:T  List].    (A  \msubseteq{}  B  \mmember{}  \mBbbP{})



Date html generated: 2016_05_14-AM-07_53_24
Last ObjectModification: 2015_12_26-PM-04_47_19

Theory : list_1


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