Nuprl Lemma : l_subset_nil_right
∀[T:Type]. ∀[L:T List]. (l_subset(T;L;[]) ⇐⇒ L = [] ∈ (T List))
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
l_subset: l_subset(T;as;bs),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
not: ¬A,
false: False,
or: P ∨ Q,
cons: [a / b]
Lemmas referenced :
all_wf,
l_member_wf,
nil_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
and_wf,
equal_wf,
list_wf,
null_wf,
btrue_neq_bfalse,
equal-wf-T-base,
list-cases,
product_subtype_list,
cons_member
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
functionEquality,
independent_isectElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
productElimination,
independent_functionElimination,
voidElimination,
baseClosed,
universeEquality,
dependent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
because_Cache,
inlFormation
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. (l\_subset(T;L;[]) \mLeftarrow{}{}\mRightarrow{} L = [])
Date html generated:
2018_05_21-PM-00_36_12
Last ObjectModification:
2017_10_11-PM-11_33_42
Theory : list_1
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