Nuprl Lemma : hd-reverse-is-last
∀[T:Type]. ∀[L:T List]. hd(rev(L)) = last(L) ∈ T supposing 0 < ||L||
Proof
Definitions occuring in Statement :
last: last(L),
hd: hd(l),
length: ||as||,
reverse: rev(as),
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
last: last(L),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
top: Top,
subtract: n - m,
squash: ↓T,
cand: A c∧ B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
list_wf,
le-add-cancel-alt,
zero-mul,
add-mul-special,
not-lt-2,
decidable__lt,
le-add-cancel,
add_functionality_wrt_le,
add-swap,
minus-minus,
minus-add,
minus-one-mul-top,
zero-add,
minus-one-mul,
condition-implies-le,
less-iff-le,
not-le-2,
subtract_wf,
decidable__le,
less_than_wf,
le_wf,
and_wf,
squash_wf,
select_wf,
add-commutes,
add-zero,
add-associates,
minus-zero,
select0,
reverse_wf,
length_wf,
lelt_wf,
length-reverse,
false_wf,
select-reverse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
minusEquality,
because_Cache,
addEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
imageElimination,
productElimination,
independent_isectElimination,
intEquality,
dependent_functionElimination,
unionElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. hd(rev(L)) = last(L) supposing 0 < ||L||
Date html generated:
2016_05_14-AM-06_41_31
Last ObjectModification:
2016_01_14-PM-08_19_46
Theory : list_0
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