Nuprl Lemma : l_disjoint_append
∀[T:Type]. ∀[a,b,c:T List]. uiff(l_disjoint(T;a;b @ c);l_disjoint(T;a;b) ∧ l_disjoint(T;a;c))
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
append: as @ bs,
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
l_disjoint: l_disjoint(T;l1;l2),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
cand: A c∧ B,
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
l_member_wf,
all_wf,
not_wf,
or_wf,
member_append,
append_wf,
uiff_wf,
l_disjoint_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
independent_pairFormation,
isect_memberFormation,
introduction,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
productElimination,
independent_functionElimination,
inlFormation,
extract_by_obid,
isectElimination,
productEquality,
voidElimination,
because_Cache,
sqequalRule,
inrFormation,
independent_pairEquality,
lambdaEquality,
addLevel,
independent_isectElimination,
cumulativity,
universeEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[a,b,c:T List]. uiff(l\_disjoint(T;a;b @ c);l\_disjoint(T;a;b) \mwedge{} l\_disjoint(T;a;c))
Date html generated:
2019_06_20-PM-01_27_06
Last ObjectModification:
2018_08_24-PM-11_13_00
Theory : list_1
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