Nuprl Lemma : extd-nameset_subtype
∀[L,L':Cname List]. extd-nameset(L) ⊆r extd-nameset(L') supposing l_subset(Cname;L;L')
Proof
Definitions occuring in Statement :
extd-nameset: extd-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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
extd-nameset: extd-nameset(L),
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
l_subset_wf,
coordinate_name_wf,
list_wf,
nameset_wf,
int_seg_wf,
nameset_subtype,
subtype_rel_self,
subtype_rel_b-union
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
axiomEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation
Latex:
\mforall{}[L,L':Cname List]. extd-nameset(L) \msubseteq{}r extd-nameset(L') supposing l\_subset(Cname;L;L')
Date html generated:
2016_05_20-AM-09_29_03
Last ObjectModification:
2015_12_28-PM-04_47_59
Theory : cubical!sets
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