Nuprl Lemma : weak_l_before_append_front
∀[T:Type]. ∀L1,L2:T List. ∀x,y:T. ((y ∈ L1) ⇒ 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],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
false: False,
prop: ℙ,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
last: last(L),
select: L[n],
list_ind: list_ind,
cons: [a / b],
subtract: n - m,
length: ||as||,
nil: [],
it: ⋅
Lemmas referenced :
l_member_wf,
sublist_wf,
cons_wf,
nil_wf,
append_wf,
not_wf,
list_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
sublist_append_front,
null_cons_lemma,
last_wf,
assert_wf,
null_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
hypothesis,
rename,
Error :universeIsType,
universeEquality,
isect_memberEquality,
voidEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]
\mforall{}L1,L2:T List. \mforall{}x,y:T. ((y \mmember{} L1) {}\mRightarrow{} x before y \mmember{} L1 @ L2 {}\mRightarrow{} x before y \mmember{} L1 supposing \mneg{}(y \mmember{} L2))
Date html generated:
2019_06_20-PM-01_23_08
Last ObjectModification:
2018_09_26-PM-05_27_48
Theory : list_1
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