Nuprl Lemma : l_before_append_front
∀[T:Type]. ∀L1,L2:T List. ∀x,y:T. x before y ∈ L1 @ L2 ⇒ x before y ∈ L1 supposing ¬(y ∈ L2)
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
l_member: (x ∈ l),
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
l_before: x before y ∈ l,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
last: last(L),
select: L[n],
cons: [a / b],
subtract: n - m,
length: ||as||,
list_ind: list_ind,
nil: [],
it: ⋅
Lemmas referenced :
l_member_wf,
sublist_append_front,
cons_wf,
nil_wf,
null_cons_lemma,
last_wf,
not_wf,
assert_wf,
null_wf,
sublist_wf,
append_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesis,
rename,
because_Cache,
independent_isectElimination,
isect_memberEquality,
voidEquality,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. \mforall{}x,y:T. x before y \mmember{} L1 @ L2 {}\mRightarrow{} x before y \mmember{} L1 supposing \mneg{}(y \mmember{} L2)
Date html generated:
2016_05_14-AM-07_44_54
Last ObjectModification:
2015_12_26-PM-02_53_05
Theory : list_1
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