Nuprl Lemma : l_subset_nil_left_true
∀[T:Type]. ∀[L:T List]. uiff(l_subset(T;[];L);True)
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
nil: [],
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
true: True,
prop: ℙ,
l_subset: l_subset(T;as;bs),
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False
Lemmas referenced :
l_subset_wf,
nil_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
l_member_wf,
true_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
introduction,
cut,
natural_numberEquality,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
rename,
lambdaFormation,
independent_isectElimination,
independent_functionElimination,
voidElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. uiff(l\_subset(T;[];L);True)
Date html generated:
2016_05_14-AM-07_53_44
Last ObjectModification:
2015_12_26-PM-04_47_45
Theory : list_1
Home
Index