Nuprl Lemma : extd-nameset_subtype_base
∀[L:Cname List]. (extd-nameset(L) ⊆r Base)
Proof
Definitions occuring in Statement :
extd-nameset: extd-nameset(L),
coordinate_name: Cname,
list: T List,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
extd-nameset: extd-nameset(L),
b-union: A ⋃ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
ifthenelse: if b then t else f fi ,
bool: 𝔹,
int_seg: {i..j-},
subtype_rel: A ⊆r B
Lemmas referenced :
tunion_subtype_base,
bool_wf,
ifthenelse_wf,
nameset_wf,
int_seg_wf,
nameset_subtype_base,
set_subtype_base,
lelt_wf,
int_subtype_base,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
instantiate,
hypothesisEquality,
universeEquality,
natural_numberEquality,
independent_isectElimination,
lambdaFormation,
unionElimination,
intEquality,
because_Cache,
axiomEquality
Latex:
\mforall{}[L:Cname List]. (extd-nameset(L) \msubseteq{}r Base)
Date html generated:
2016_05_20-AM-09_28_59
Last ObjectModification:
2015_12_28-PM-04_47_57
Theory : cubical!sets
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