Nuprl Lemma : l_disjoint_nil_iff
∀[A:Type]. ∀[L:A List]. (l_disjoint(A;L;[]) ⇐⇒ True)
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
true: True,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
l_disjoint: l_disjoint(T;l1;l2),
all: ∀x:A. B[x],
not: ¬A,
false: False
Lemmas referenced :
l_disjoint_wf,
nil_wf,
l_disjoint_nil2,
true_wf,
and_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
voidElimination,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List]. (l\_disjoint(A;L;[]) \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2016_05_14-AM-07_56_04
Last ObjectModification:
2015_12_26-PM-04_50_11
Theory : list_1
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