Nuprl Lemma : poset-cat-ob_subtype
∀[I,J:Cname List]. cat-ob(poset-cat(I)) ⊆r cat-ob(poset-cat(J)) supposing nameset(J) ⊆r nameset(I)
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
nameset: nameset(L),
coordinate_name: Cname,
cat-ob: cat-ob(C),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
poset-cat: poset-cat(J),
cat-ob: cat-ob(C),
pi1: fst(t),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
name-morph_subtype,
nil_wf,
coordinate_name_wf,
nameset_wf,
subtype_rel_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
lambdaEquality,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I,J:Cname List]. cat-ob(poset-cat(I)) \msubseteq{}r cat-ob(poset-cat(J)) supposing nameset(J) \msubseteq{}r nameset(I)
Date html generated:
2016_06_16-PM-06_52_13
Last ObjectModification:
2015_12_28-PM-04_23_07
Theory : cubical!sets
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