Nuprl Lemma : l_contains_disjoint
∀[T:Type]. ∀[A,B,C:T List]. (l_disjoint(T;B;C)) supposing (l_disjoint(T;A;C) and B ⊆ A)
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
l_contains: A ⊆ B,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
l_disjoint: l_disjoint(T;l1;l2),
l_contains: A ⊆ B,
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q
Lemmas referenced :
l_member_wf,
all_wf,
not_wf,
l_all_iff,
l_all_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
independent_pairFormation,
productElimination,
promote_hyp,
voidElimination,
productEquality,
extract_by_obid,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
addLevel,
independent_isectElimination,
setElimination,
rename,
setEquality,
cumulativity,
isectEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[A,B,C:T List]. (l\_disjoint(T;B;C)) supposing (l\_disjoint(T;A;C) and B \msubseteq{} A)
Date html generated:
2019_06_20-PM-01_27_01
Last ObjectModification:
2018_08_24-PM-11_15_23
Theory : list_1
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