Nuprl Lemma : l_subset_nil_left
∀[T:Type]. ∀[L:T List]. l_subset(T;[];L)
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
l_subset: l_subset(T;as;bs),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. l\_subset(T;[];L)
Date html generated:
2016_05_14-AM-07_53_49
Last ObjectModification:
2015_12_26-PM-04_47_48
Theory : list_1
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