Nuprl Lemma : l_disjoint-symmetry
∀[T:Type]. ∀[a,b:T List]. uiff(l_disjoint(T;b;a);l_disjoint(T;a;b))
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
l_disjoint: l_disjoint(T;l1;l2),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
cand: A c∧ B,
false: False,
prop: ℙ
Lemmas referenced :
and_wf,
l_member_wf,
l_disjoint_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
productElimination,
voidElimination,
lemma_by_obid,
isectElimination,
sqequalRule,
lambdaEquality,
because_Cache,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:T List]. uiff(l\_disjoint(T;b;a);l\_disjoint(T;a;b))
Date html generated:
2016_05_14-AM-07_55_41
Last ObjectModification:
2015_12_26-PM-04_49_39
Theory : list_1
Home
Index