Nuprl Lemma : l_disjoint_nil2
∀[A:Type]. ∀[L:A List]. l_disjoint(A;L;[])
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
l_disjoint: l_disjoint(T;l1;l2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
and_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
lemma_by_obid,
hypothesis,
isectElimination,
hypothesisEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List]. l\_disjoint(A;L;[])
Date html generated:
2016_05_14-AM-07_55_59
Last ObjectModification:
2015_12_26-PM-04_49_59
Theory : list_1
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