Nuprl Lemma : l_disjoint_intersection
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a,b,c:T List].
l_disjoint(T;l_intersection(eq;b;c);a) supposing l_disjoint(T;b;a) ∨ l_disjoint(T;c;a)
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,
l_disjoint: l_disjoint(T;l1;l2),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
or: P ∨ Q,
cand: A c∧ B,
prop: ℙ,
iff: P ⇐⇒ Q
Lemmas referenced :
and_wf,
l_member_wf,
member-intersection,
l_intersection_wf,
not_wf,
or_wf,
l_disjoint_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
thin,
productElimination,
unionElimination,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
independent_pairFormation,
voidElimination,
lemma_by_obid,
isectElimination,
addLevel,
impliesFunctionality,
andLevelFunctionality,
sqequalRule,
lambdaEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a,b,c:T List].
l\_disjoint(T;l\_intersection(eq;b;c);a) supposing l\_disjoint(T;b;a) \mvee{} l\_disjoint(T;c;a)
Date html generated:
2016_05_14-PM-03_32_35
Last ObjectModification:
2015_12_26-PM-06_01_16
Theory : decidable!equality
Home
Index