Nuprl Lemma : subtype-add-fresh-cname
∀[I:Cname List]. (nameset(I) ⊆r nameset(I+))
Proof
Definitions occuring in Statement :
add-fresh-cname: I+,
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
add-fresh-cname: I+,
has-value: (a)↓,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
value-type-has-value,
coordinate_name_wf,
not_wf,
l_member_wf,
set-value-type,
coordinate_name-value-type,
fresh-cname_wf,
nameset_subtype,
cons_wf,
l_subset_right_cons_trivial,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
lambdaEquality,
applyEquality,
because_Cache,
dependent_functionElimination,
setElimination,
rename,
axiomEquality
Latex:
\mforall{}[I:Cname List]. (nameset(I) \msubseteq{}r nameset(I+))
Date html generated:
2016_05_20-AM-09_28_54
Last ObjectModification:
2015_12_28-PM-04_48_04
Theory : cubical!sets
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