### Nuprl Lemma : nameset_subtype

`∀[L1,L2:Cname List].  nameset(L1) ⊆r nameset(L2) supposing l_subset(Cname;L1;L2)`

Proof

Definitions occuring in Statement :  nameset: `nameset(L)` coordinate_name: `Cname` l_subset: `l_subset(T;as;bs)` list: `T List` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  nameset: `nameset(L)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` l_subset: `l_subset(T;as;bs)`
Lemmas referenced :  subtype_rel_sets coordinate_name_wf l_member_wf l_subset_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesis because_Cache lambdaEquality hypothesisEquality independent_isectElimination setElimination rename setEquality lambdaFormation dependent_functionElimination independent_functionElimination axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[L1,L2:Cname  List].    nameset(L1)  \msubseteq{}r  nameset(L2)  supposing  l\_subset(Cname;L1;L2)

Date html generated: 2016_05_20-AM-09_28_14
Last ObjectModification: 2015_12_28-PM-04_48_24

Theory : cubical!sets

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