Nuprl Lemma : remove-repeats-fun-length-as-remove-repeats-map
∀[A,B:Type]. ∀[eq:EqDecider(B)]. ∀[f:A ⟶ B]. ∀[L:A List].
(||remove-repeats-fun(eq;f;L)|| = ||remove-repeats(eq;map(f;L))|| ∈ ℤ)
Proof
Definitions occuring in Statement :
remove-repeats-fun: remove-repeats-fun(eq;f;L),
remove-repeats: remove-repeats(eq;L),
length: ||as||,
map: map(f;as),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
true: True,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
length-map,
remove-repeats-fun_wf,
deq_wf,
length_wf,
remove-repeats_wf,
map_wf,
equal_wf,
squash_wf,
true_wf,
remove-repeats-fun-as-remove-repeats-map,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
cumulativity,
functionExtensionality,
applyEquality,
hypothesis,
because_Cache,
sqequalRule,
axiomEquality,
functionEquality,
universeEquality,
intEquality,
natural_numberEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[eq:EqDecider(B)]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[L:A List].
(||remove-repeats-fun(eq;f;L)|| = ||remove-repeats(eq;map(f;L))||)
Date html generated:
2017_04_17-AM-09_11_57
Last ObjectModification:
2017_02_27-PM-05_19_23
Theory : decidable!equality
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