### Nuprl Lemma : subtype_rel_list

`∀[A,B:Type].  (A List) ⊆r (B List) supposing A ⊆r B`

Proof

Definitions occuring in Statement :  list: `T List` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` list: `T List` so_lambda: `λ2x.t[x]` nat: `ℕ` so_apply: `x[s]` all: `∀x:A. B[x]` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r B`
Lemmas referenced :  subtype_rel_sets colist_wf has-value_wf-partial nat_wf set-value-type le_wf int-value-type colength_wf subtype_rel_set subtype_rel_colist subtype_rel_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis sqequalRule lambdaEquality independent_isectElimination intEquality natural_numberEquality cumulativity because_Cache lambdaFormation axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[A,B:Type].    (A  List)  \msubseteq{}r  (B  List)  supposing  A  \msubseteq{}r  B

Date html generated: 2016_05_14-AM-06_25_45
Last ObjectModification: 2015_12_26-PM-00_42_25

Theory : list_0

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