Nuprl Lemma : l_before_member
∀[T:Type]. ∀L:T List. ∀a,b:T. (a before b ∈ L ⇒ (b ∈ L))
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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,
member: t ∈ T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
not: ¬A,
false: False
Lemmas referenced :
sublist_wf,
cons_wf,
nil_wf,
list_wf,
member_iff_sublist,
sublist_transitivity,
sublist_tl,
null_cons_lemma,
false_wf,
reduce_tl_cons_lemma,
sublist_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :universeIsType,
universeEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}a,b:T. (a before b \mmember{} L {}\mRightarrow{} (b \mmember{} L))
Date html generated:
2019_06_20-PM-01_23_12
Last ObjectModification:
2018_09_26-PM-05_27_51
Theory : list_1
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