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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