Nuprl Lemma : l_disjoint_singleton2
∀[T:Type]. ∀[a:T List]. ∀[x:T]. uiff(l_disjoint(T;[x];a);¬(x ∈ a))
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
l_member: (x ∈ l),
cons: [a / b],
nil: [],
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
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,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q,
l_disjoint: l_disjoint(T;l1;l2),
all: ∀x:A. B[x]
Lemmas referenced :
l_disjoint_singleton,
iff_weakening_uiff,
l_disjoint_wf,
cons_wf,
nil_wf,
l_disjoint-symmetry,
l_member_wf,
and_wf,
not_wf,
uiff_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
addLevel,
productElimination,
independent_pairFormation,
introduction,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
voidElimination,
cumulativity,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T List]. \mforall{}[x:T]. uiff(l\_disjoint(T;[x];a);\mneg{}(x \mmember{} a))
Date html generated:
2016_05_14-AM-07_55_50
Last ObjectModification:
2015_12_26-PM-04_49_56
Theory : list_1
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