Nuprl Lemma : l_disjoint_intersection2
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a,b,c:T List].
l_disjoint(T;a;l_intersection(eq;b;c)) supposing l_disjoint(T;a;b) ∨ l_disjoint(T;a;c)
Proof
Definitions occuring in Statement :
l_intersection: l_intersection(eq;L1;L2),
l_disjoint: l_disjoint(T;l1;l2),
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
or: P ∨ Q,
prop: ℙ,
guard: {T},
l_disjoint: l_disjoint(T;l1;l2),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
l_disjoint-symmetry,
l_intersection_wf,
l_disjoint_intersection,
l_disjoint_wf,
and_wf,
l_member_wf,
or_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
because_Cache,
unionElimination,
inlFormation,
sqequalRule,
inrFormation,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a,b,c:T List].
l\_disjoint(T;a;l\_intersection(eq;b;c)) supposing l\_disjoint(T;a;b) \mvee{} l\_disjoint(T;a;c)
Date html generated:
2016_05_14-PM-03_32_38
Last ObjectModification:
2015_12_26-PM-06_01_03
Theory : decidable!equality
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