Nuprl Lemma : nameset_subtype_cons_diff
∀[I:Cname List]. ∀[x:nameset(I)]. (nameset(I) ⊆r nameset([x / I-[x]]))
Proof
Definitions occuring in Statement :
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
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,
nameset: nameset(L),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
l_subset: l_subset(T;as;bs),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
guard: {T},
cand: A c∧ B
Lemmas referenced :
nameset_subtype,
cons_wf,
coordinate_name_wf,
list-diff_wf,
cname_deq_wf,
nil_wf,
nameset_wf,
list_wf,
l_member_wf,
cons_member,
member_singleton,
or_wf,
equal_wf,
and_wf,
not_wf,
member-list-diff,
decidable__equal-coordinate_name
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
lambdaFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination,
addLevel,
orFunctionality,
independent_pairFormation,
impliesFunctionality,
andLevelFunctionality,
impliesLevelFunctionality,
unionElimination,
inlFormation,
inrFormation
Latex:
\mforall{}[I:Cname List]. \mforall{}[x:nameset(I)]. (nameset(I) \msubseteq{}r nameset([x / I-[x]]))
Date html generated:
2016_05_20-AM-09_28_16
Last ObjectModification:
2015_12_28-PM-04_48_30
Theory : cubical!sets
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