Nuprl Lemma : l_disjoint_singleton
∀[T:Type]. ∀[a:T List]. ∀[x:T]. uiff(l_disjoint(T;a;[x]);¬(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],
l_disjoint: l_disjoint(T;l1;l2),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
l_member_wf,
all_wf,
not_wf,
equal_wf,
member_singleton,
cons_wf,
nil_wf,
uiff_wf,
list_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
independent_pairFormation,
introduction,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
productEquality,
productElimination,
because_Cache,
addLevel,
independent_isectElimination,
cumulativity,
universeEquality,
hyp_replacement,
equalitySymmetry,
dependent_set_memberEquality,
applyLambdaEquality,
setElimination,
rename
Latex:
\mforall{}[T:Type]. \mforall{}[a:T List]. \mforall{}[x:T]. uiff(l\_disjoint(T;a;[x]);\mneg{}(x \mmember{} a))
Date html generated:
2019_06_20-PM-01_27_16
Last ObjectModification:
2018_08_24-PM-11_25_52
Theory : list_1
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