Nuprl Lemma : sublist-same-last
∀[T:Type]. ∀[L,L':T List].
(last(L') = last(L) ∈ T) supposing ((last(L) ∈ L') and L' ⊆ L and (¬↑null(L')) and no_repeats(T;L) and (¬↑null(L)))
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
last: last(L),
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
false: False,
guard: {T}
Lemmas referenced :
l_tricotomy,
last_wf,
last_member,
l_member_wf,
sublist_wf,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
no_repeats_wf,
last-not-before,
no_repeats-sublist,
l_before_sublist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_isectElimination,
hypothesis,
independent_functionElimination,
because_Cache,
unionElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
voidElimination,
voidEquality,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}[L,L':T List].
(last(L') = last(L)) supposing
((last(L) \mmember{} L') and
L' \msubseteq{} L and
(\mneg{}\muparrow{}null(L')) and
no\_repeats(T;L) and
(\mneg{}\muparrow{}null(L)))
Date html generated:
2016_05_15-PM-03_42_17
Last ObjectModification:
2015_12_27-PM-01_18_39
Theory : general
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